{"version":3,"sources":["webpack:///./src/components/physics/springs/springmass/Spring.vue","webpack:///./src/components/physics/springs/springmass/Boxes.js","webpack:///src/components/physics/springs/springmass/Spring.vue","webpack:///./src/components/physics/springs/springmass/Spring.vue?c8f3","webpack:///./src/components/physics/springs/springmass/Spring.vue?55a7"],"names":["staticClass","class","_vm","$vuetify","_c","staticStyle","ref","attrs","staticRenderFns","render","Boxes","box1","board","JXG","JSXGraph","initBoard","boundingbox","keepaspectratio","axis","grid","ticks","showCopyright","showNavigation","pan","enabled","zoom","options","minimizeReflow","text","highlight","fixed","image","cssDefaultStyle","line","curve","point","showInfoBox","layer","makeResponsive","placeLogo","placeTitle","create","strokeColor","strokeWidth","Math","round","canvasWidth","withLabel","name","straightFirst","straightLast","lastArrow","label","display","fontSize","canvasHeight","CssStyle","position","offset","visible","size","face","msg1","Y","cssStyle","anchorX","writeMiddleText","setAttribute","color","msg2","m","add","remove","on","alert","moveTo","stopAllAnimation","Pt0","vis","viss","k","addK","removeK","valueOf","isInDragMode","i","numberOfSpringRings","springRings","fillColor","fillOpacity","withLines","vertices","startAnimation","startY","moveAlong","dt","duration","PI","t","a","cos","startPlotting","half","sqrt","Pt1","abs","min","X","toFixed","anchorY","Pt2","x","Pt3","drawPoint","Pt4","hook","mode","BOARD_MODE_DRAG","drawSegment","addHook","created","_this","title","$store","commit","newTopics","img","action","goto","newshowhome","newPhys","newLeftArrow","newModule","mounted","MathJax","Hub","Queue","metaInfo","titleTemplate","meta","content","component"],"mappings":"mJAA4D,EAAU,W,IAAiBA,OAAgCC,EAAK,EAAC,S,OAAC,WAAiBC,MAAIC,C,YAA4B,oB,MAAmD,CAAgD,8CAAIC,kBAAS,6BAACJ,cAAY,sBAAoB,Y,CAAQ,S,YAAuD,qB,MAAkC,CAA+C,0CAAII,SAAU,6BAACC,WAAY,kCAAuB,WAAE,YAAS,CAAqCC,cAAQ,W,CAAc,gCAAa,SAAM,SAAG,YAAQ,CAAqZA,aAAQ,UAAc,gZAAa,SAAM,SAAG,YAAU,CAACN,aAAY,UAA4B,S,YAAuD,qB,MAAkC,CAA+C,0CAAII,SAAU,6BAACC,WAAY,kCAAuB,WAAE,YAAS,CAAqDC,cAAQ,W,CAAc,gDAAa,SAAM,SAAG,YAAQ,CAA85CA,aAAQ,UAAc,6UAAa,+kCAAM,SAAG,YAAU,CAACN,aAAY,UAA4B,S,YAAuD,qB,MAAkC,CAA+C,0CAAII,SAAU,6BAACC,WAAY,kCAAuB,WAAE,YAAS,CAA0DC,cAAQ,W,CAAc,qDAAa,SAAM,SAAG,YAAQ,CAAiOA,aAAQ,UAAc,4NAAa,SAAM,SAAG,YAAU,CAACN,aAAY,UAA4B,S,YAAuD,qB,MAAkC,CAA+C,0CAAII,SAAU,6BAACC,WAAY,kCAAuB,WAAE,YAAS,CAA2DC,cAAQ,W,CAAc,sDAAa,SAAM,SAAG,YAAQ,CAA4MC,aAAM,UAAoB,mMAAE,MAAK,CAAOP,iBAAY,K,CAAyB,QAAK,CAAS,8BAAG,MAAM,CAAYO,GAAM,eAAoB,UAAE,MAAK,CAAMP,iBAAY,KAC1pI,SACGQ,gCAEJ,GAASC,oJAAuB,Q,iBCsC1BC,EAAQ,CACZC,KAAM,WACJ,IAAIC,EAAQC,IAAIC,SAASC,UAAU,UAAW,CAACC,YAAa,EAAE,EAAG,GAAI,GAAI,GAAIC,iBAAiB,EAAMC,MAAK,EAAOC,MAAK,EAAMC,OAAM,EAAOC,eAAc,EAAOC,gBAAe,EAAOC,IAAI,CAACC,SAAQ,GAAQC,KAAK,CAACD,SAAQ,KAEtNZ,EAAMc,QAAQd,MAAMe,eAAiB,OACrCf,EAAMc,QAAQE,KAAKC,WAAU,EAC7BjB,EAAMc,QAAQE,KAAKE,OAAM,EACzBlB,EAAMc,QAAQK,MAAMF,WAAU,EAC9BjB,EAAMc,QAAQE,KAAKI,gBAAgB,oBACnCpB,EAAMc,QAAQO,KAAKJ,WAAU,EAC7BjB,EAAMc,QAAQQ,MAAML,WAAU,EAC9BjB,EAAMc,QAAQS,MAAMN,WAAU,EAC9BjB,EAAMc,QAAQS,MAAMC,aAAY,EAEhCxB,EAAMc,QAAQW,MAAM,SAAU,GAE9BC,eAAe1B,GACf2B,eAAU3B,GACV4B,eAAW5B,EAAO,qBAAsB,qCAE7BA,EAAM6B,OAAO,OAAQ,CAAC,CAAC,EAAG,GAAG,CAAC,EAAG,IAAK,CAAEC,YAAY,OAC7Db,WAAU,EAAOc,YAAa,kBAAIC,KAAKC,MAAM,EAAEjC,EAAMkC,YAAY,MACjEC,WAAU,EAAMC,KAAM,GAAIC,eAAc,EAAOC,cAAa,EAAMC,WAAU,EAC1EC,MAAO,CACLC,QAAQ,WACRC,SAAS,WAAW,OAAO,GAAG1C,EAAM2C,aAAa,KACjDC,SAAU,oCACVC,SAAU,KACVC,OAAQ,EAAE,GAAI,OAGX9C,EAAM6B,OAAO,OAAQ,CAAC,CAAC,GAAI,GAAG,CAAC,EAAG,IAAK,CAAEC,YAAY,OACxDb,WAAU,EAAOc,YAAa,kBAAIC,KAAKC,MAAM,EAAEjC,EAAMkC,YAAY,MACjEC,WAAU,EAAMC,KAAM,GAAIC,eAAc,EAAOC,cAAa,EAAOC,WAAU,EAC3EC,MAAO,CACLC,QAAQ,WACRC,SAAS,WAAW,OAAO,GAAG1C,EAAM2C,aAAa,KACjDC,SAAU,oCACVC,SAAU,KACVC,OAAQ,EAAE,GAAI,OAnBxB,IAoBIzB,EAAOrB,EAAM6B,OAAO,OAAQ,CAAC,EAAE,IAAI,GAAI,EAAE,KAAM,IAAK,CAACkB,SAAS,EAAOV,eAAe,EAAOC,cAAc,IAEzGf,EAAQvB,EAAM6B,OAAO,SAAU,EAAE,IAAK,EAAGR,GAAO,CAACe,KAAM,GAAIY,KAAK,WAAW,OAAO,GAAGhD,EAAM2C,aAAa,KAAMM,KAAK,WAQnHC,GANOlD,EAAM6B,OAAO,OAAO,EAAE,IAAK,WAAW,OAAQ,EAAEN,EAAM4B,KAAK,GAAM,KAAK,CAACV,QAAQ,WAAYW,SAAS,oBAAoBV,SAAS,WAAW,OAAOV,KAAKC,MAAM,GAAGjC,EAAMkC,YAAY,MAAQhB,OAAM,IAEjMlB,EAAM6B,OAAO,OAAO,EAAE,IAAK,WAAW,OAAON,EAAM4B,KAAM,KAAK,CAACV,QAAQ,WAAYY,QAAQ,SAAUD,SAAS,oBAAoBV,SAAS,WAAW,OAAOV,KAAKC,MAAM,GAAGjC,EAAMkC,YAAY,MAAQhB,OAAM,IAE3MlB,EAAM6B,OAAO,OAAO,EAAE,EAAG,IAAK,OAAO,CAACY,QAAQ,OAAQY,QAAQ,SAAUD,SAAS,oBAAoBV,SAAS,WAAW,OAAOV,KAAKC,MAAM,GAAGjC,EAAMkC,YAAY,MAAQhB,OAAM,IAE/KoC,eAAgBtD,EAAO,IAAK,IAAK,wBAC3CkD,EAAKK,aAAa,CAACC,MAAM,MAAOT,SAAQ,IAExC,IAAIU,EAAMH,eAAgBtD,EAAO,IAAK,IAAK,uBAC3CyD,EAAKF,aAAa,CAACC,MAAM,MAAOT,SAAQ,IAExC,IAAIW,EAAE,IACFC,EAAM3D,EAAM6B,OAAO,QAAS,CAAC,mBAAoB,EAAE,EAAI,OAAU,CAAC,IAAM,MAAO,CAACX,OAAM,IACtF0C,EAAS5D,EAAM6B,OAAO,QAAS,CAAC,qBAAsB,EAAE,KAAM,OAAU,CAAC,IAAM,MAAO,CAACX,OAAM,IAEjGyC,EAAIE,GAAG,QAAO,WAAcH,EAAE,EAAQA,GAAG,KAAYA,EAAE,EAAQI,eAAM9D,EAAOkD,IAAQ3B,EAAMwC,OAAO,EAAE,IAAK,IAAM/D,EAAMgE,mBAAoBC,EAAIF,OAAO,CAAC,EAAG,kBAAIxC,EAAM4B,OAAOe,GAAI,EAAOC,GAAK,KACxLP,EAAOC,GAAG,QAAO,WAAcH,EAAE,IAAQA,GAAG,KAAaA,EAAE,IAAQI,eAAM9D,EAAOyD,IAAQlC,EAAMwC,OAAO,EAAE,IAAK,IAAM/D,EAAMgE,mBAAoBC,EAAIF,OAAO,CAAC,EAAG,kBAAIxC,EAAM4B,OAAOe,GAAI,EAAOC,GAAK,KAE5L,IAAIC,EAAE,EACFC,EAAOrE,EAAM6B,OAAO,QAAS,CAAC,mBAAoB,EAAE,EAAI,OAAU,CAAC,IAAM,MAAO,CAACX,OAAM,IACvFoD,EAAUtE,EAAM6B,OAAO,QAAS,CAAC,qBAAsB,EAAE,KAAK,OAAU,CAAC,IAAM,MAAO,CAACX,OAAM,IACjGmD,EAAKR,GAAG,QAAO,WAAcO,EAAE,EAAGA,GAAG,GAAOA,EAAE,EAAGN,eAAM9D,EAAOkD,IAAO3B,EAAMwC,OAAO,EAAE,IAAK,IAAM/D,EAAMgE,mBAAoBC,EAAIF,OAAO,CAAC,EAAG,kBAAIxC,EAAM4B,OAAOe,GAAI,EAAOC,GAAK,KACzKG,EAAQT,GAAG,QAAO,WAAcO,EAAE,EAAGA,GAAG,GAAQA,EAAE,EAAGN,eAAM9D,EAAOyD,IAAQlC,EAAMwC,OAAO,EAAE,IAAK,IAAM/D,EAAMgE,mBAAoBC,EAAIF,OAAO,CAAC,EAAG,kBAAIxC,EAAM4B,OAAOe,GAAI,EAAOC,GAAK,KAE9KnE,EAAM6B,OAAO,OAAO,EAAE,EAAI,EAAG,iBAAI,OAAO6B,EAAEa,UAAU,QAAO,CAAC9B,QAAQ,WAAYY,QAAQ,SAAUG,MAAM,MAAOJ,SAAS,oBAAoBV,SAAS,WAAW,OAAOV,KAAKC,MAAM,GAAGjC,EAAMkC,YAAY,MAAQhB,OAAM,IAErNlB,EAAM6B,OAAO,OAAO,EAAE,EAAI,EAAG,iBAAI,OAAOuC,EAAEG,UAAU,SAAQ,CAAC9B,QAAQ,WAAYY,QAAQ,SAAUG,MAAM,OAAQJ,SAAS,oBAAoBV,SAAS,WAAW,OAAOV,KAAKC,MAAM,GAAGjC,EAAMkC,YAAY,MAAQhB,OAAM,IAEvN,IAAIsD,GAAe,EAIfC,GAFezE,EAAM6B,OAAO,QAAS,CAAC,EAAG,GAAI,CAAC2B,MAAO,QAASpB,KAAM,GAAIlB,OAAO,EAAM6B,SAAQ,IAE3F,GACF2B,EAAsB,GACtBC,EAAc,GAElB,IAAIF,EAAE,EAAGA,EAAEC,EAAqBD,IAC5BE,EAAYF,GAAKzE,EAAM6B,OAAO,QAAS,CAAM,IAAK4C,EAAE,EAAE,IAAb,IAAmB,SAASA,GAAG,OAAO,WAAW,OAAO,GAAI,EAAElD,EAAM4B,KAAKuB,EAAqBD,GAA3E,CAAgFA,IAAK,CAACtC,WAAU,EAAOY,SAAQ,EAAOS,MAAO,QAASR,KAAM,IACnMyB,EAAE,GACHzE,EAAM6B,OAAO,UAAW,CAAC8C,EAAYF,EAAE,GAAIE,EAAYF,IAAK,CAACjB,MAAM,OAAQzB,YAAY,kBAAI,EAAE/B,EAAMkC,YAAY,OAI7GlC,EAAM6B,OAAO,UAAU,CAAC,EAAE,EAAE,GAAG,EAAE,EAAG,GAAG,EAAE,EAAG,GAAG,EAAE,EAAG,IAAK,CAAC+C,UAAU,YAAaC,YAAY,GAAKC,WAAU,EAAOC,SAAS,CAAChC,SAAQ,KAQ/I,SAASiC,EAAeC,GACxB1D,EAAM2D,UAAU,WAChB,IAAIC,EAAK,IACLC,EAAW,GAAGD,EAAG,EAAEnD,KAAKqD,GAAG3B,EAAEa,UAAUH,EAAEG,UAC7C,OAAO,SAASe,GACZ,OAAIA,GAAKF,EAEE,CAAC,EAAG,IAGfG,EAAGN,EACI,EAAE,IAAKA,EAAOjD,KAAKwD,IAAKpB,EAAEG,UAAUb,EAAEa,UAAWe,EAAEH,MAV9C,IAPhBnF,EAAM6B,OAAO,QAAS,EAAE,IAAK,IAAM,CAACO,KAAM,GAAIoB,MAAM,OAAQR,KAAK,WAAW,OAAO,EAAEhD,EAAM2C,aAAa,KAAMM,KAAK,iBAEnHjD,EAAM6B,OAAO,QAAS,EAAE,IAAK,KAAM,CAACO,KAAM,GAAIoB,MAAM,OAAQR,KAAK,WAAW,OAAO,EAAEhD,EAAM2C,aAAa,KAAMM,KAAK,aAAc/B,OAAM,IAEvIlB,EAAM6B,OAAO,UAAW,CAAC,EAAE,IAAK,GAAG,EAAE,IAAK,IAAM,CAACX,OAAM,EAAMY,YAAY,QAASC,YAAY,IAiBhG,IAAIwD,EAAG,EAAOrB,GAAI,EACdD,EAAMjE,EAAM6B,OAAO,QAAS,CAAC,EAAG,GAAI,CAACO,KAAM,GAAIoB,MAAM,QAAQT,QAAQ,kBAAS,GAALmB,GAAiB,GAANC,GAAYnB,KAAK,WAAW,OAAO,EAAEhD,EAAM2C,aAAa,KAAMM,KAAK,iBAE3J,SAASwC,EAAcR,GACvBhB,EAAIiB,UAAU,WACd,IAAIC,EAAK,IACLC,EAAW,GAAGD,EAAG,EAAEnD,KAAKqD,GAAG3B,EAAEa,UAAUH,EAAEG,UACzCmB,EAAO,EAAEP,EAAGnD,KAAK2D,KAAKjC,EAAEa,UAAUH,EAAEG,WAClBvC,KAAK2D,KAAKjC,EAAEa,UAAUH,EAAEG,WAC9C,OAAO,SAASe,GACZ,KAAIA,GAAKF,GAKJ,OAAIE,GAAGI,GACVvB,GAAK,EACLD,GAAM,EACC,CAACoB,EAAEH,EAAInD,KAAK2D,KAAKjC,EAAEa,UAAUH,EAAEG,WAAY,EAAGU,EAAOjD,KAAKwD,IAAKpB,EAAEG,UAAUb,EAAEa,UAAWe,EAAEH,MAGnGI,EAAGN,EACHf,GAAI,EACJC,GAAK,EACE,CAACmB,EAAEH,EAAInD,KAAK2D,KAAKjC,EAAEa,UAAUH,EAAEG,WAAaU,EAAOjD,KAAKwD,IAAKpB,EAAEG,UAAUb,EAAEa,UAAWe,EAAEH,KAb3FhB,GAAK,GAPC,IAyBd,IAAIyB,EAAM5F,EAAM6B,OAAO,QAAS,CAAC,GAAO,kBAAK,KAAKG,KAAK6D,IAAIN,KAAK,CAACnD,KAAM,GAAIoB,MAAM,QAAQT,QAAQ,kBAAS,GAALmB,GAAiB,GAANC,GAAYnB,KAAK,WAAW,OAAO,EAAEhD,EAAM2C,aAAa,KAAMM,KAAK,iBAEnLjD,EAAM6B,OAAO,OAAO,CAAC,kBAAY,EAARG,KAAKqD,GAAKrD,KAAK2D,KAAKjC,EAAEa,UAAUH,EAAEG,WAAW,GAAG,kBAAK,IAAIvC,KAAK6D,IAAIN,IAAI,iBAAI,OAAOvD,KAAK8D,IAAI7B,EAAI8B,IAAa,EAAR/D,KAAKqD,GAAKrD,KAAK2D,KAAKjC,EAAEa,UAAUH,EAAEG,YAAYyB,QAAQ,GAAG,SAAQ,CAACjD,QAAQ,kBAAS,GAALmB,GAAiB,GAANC,GAAY1B,QAAQ,WACzOwD,QAAQ,MAAO5C,QAAQ,SAAUD,SAAS,oBAAoBV,SAAS,WAAW,OAAOV,KAAKC,MAAM,GAAGjC,EAAMkC,YAAY,MAAQhB,OAAM,IAEvI,IAAIgF,EAAKlG,EAAM6B,OAAO,QAAS,CAAC,kBAAIG,KAAK8D,IAAI7B,EAAI8B,IAAa,EAAR/D,KAAKqD,GAAKrD,KAAK2D,KAAKjC,EAAEa,UAAUH,EAAEG,aAAa,kBAAK,KAAKvC,KAAK6D,IAAIN,KAAK,CAACnD,KAAM,GAAIW,QAAQ,kBAAS,GAALmB,GAAiB,GAANC,GAAYX,MAAM,QAASR,KAAK,WAAW,OAAO,EAAEhD,EAAM2C,aAAa,KAAMM,KAAK,gBAAiB/B,OAAM,IAEpQiD,GAAK,EACEnE,EAAM6B,OAAO,gBAAiB,CAAC,SAASsE,GAAG,OAAOZ,EAAEvD,KAAKwD,IAAIxD,KAAK2D,KAAKvB,EAAEG,UAAUb,EAAEa,WAAW4B,IAAK,EAAG,kBAAIlC,EAAI8B,MAAK,CAAChD,QAAQ,kBAAS,GAALmB,GAAUpC,YAAY,OAAQC,YAAY,kBAAI,EAAE/B,EAAMkC,YAAY,OAC/MlC,EAAM6B,OAAO,gBAAiB,CAAC,SAASsE,GAAG,OAAOZ,EAAEvD,KAAKwD,IAAIxD,KAAK2D,KAAKvB,EAAEG,UAAUb,EAAEa,YAAY4B,EAAE,KAAM,EAAG,kBAAIlC,EAAI8B,MAAK,CAAChD,QAAQ,kBAAU,GAANoB,GAAWrC,YAAY,OAAQC,YAAY,kBAAI,EAAE/B,EAAMkC,YAAY,OAEzM,IAAIkE,EAAIC,eAAUrG,GAAQ,IAAK,GAAGuD,aAAa,CAACR,SAAQ,IACpDuD,EAAID,eAAUrG,GAAQ,IAAK,GAAGuD,aAAa,CAACR,SAAQ,IAQtD,SAASwD,IACH/B,GACCxE,EAAMwG,OAASxG,EAAMyG,kBACxBjC,GAAe,EACfxE,EAAMgE,oBAEPQ,GACAxE,EAAMwG,OAASxG,EAAMyG,kBACpBjC,GAAe,EACfQ,EAAezD,EAAM4B,KACrBsC,EAAclE,EAAM4B,MAhB1BuD,eAAY1G,EAAOoG,EAAKE,GAAK/C,aAAa,CAACzB,YAAY,SAEvD4E,eAAY1G,EAAO4F,EAAKM,GAAK3C,aAAa,CAACR,QAAQ,kBAAS,GAALmB,GAAiB,GAANC,KAkBhEnE,EAAM2G,QAAQJ,KAGHzG,IC/IA,GACfsC,KAAA,YACAwE,QAAA,eAAAC,EAAA,KAEAC,EAAA,qBACA,KAAAC,OAAAC,OAAA,yBAAAF,GACA,KAAAC,OAAAC,OAAA,wBAAAF,GACA,IAAAG,EAAA,CACA,CAAAH,MAAA,qBAAAI,IAAA,uBAAAC,OAAA,kBAAAN,EAAAO,KAAA,QACA,CAAAN,MAAA,eAAAI,IAAA,uBAAAC,OAAA,kBAAAN,EAAAO,KAAA,QACA,CAAAN,MAAA,sBAAAI,IAAA,oBAAAC,OAAA,kBAAAN,EAAAO,KAAA,gBAEA,KAAAL,OAAAC,OAAA,2BAAAC,GACA,IAAAI,GAAA,EACA,KAAAN,OAAAC,OAAA,4BAAAK,GACA,IAAAC,GAAA,EACA,KAAAP,OAAAC,OAAA,yBAAAM,GACA,IAAAC,GAAA,EACA,KAAAR,OAAAC,OAAA,8BAAAO,GACA,IAAAC,GAAA,EACA,KAAAT,OAAAC,OAAA,2BAAAQ,IAEAC,QAAA,WACAC,QAAAC,IAAAC,MAAA,WAAAF,QAAAC,MACA7H,EAAAC,QAEA8H,SAAA,WACA,OAAAf,MAAA,qBACAgB,cAAA,2BACAC,KAAA,EAAA3F,KAAA,WAAA4F,QAAA,uCACA,CAAA5F,KAAA,cAAA4F,QAAA,sCC1G6X,I,YCOzXC,EAAY,eACd,EACA,EACArI,GACA,EACA,KACA,KACA,MAIa,aAAAqI,E","file":"js/chunk-2d230484.1e96f859.js","sourcesContent":["var render = function render(){var _vm=this,_c=_vm._self._c;return _c('div',[_c('div',{staticClass:\"font-weight-light\",class:{'pa-5 headline': _vm.$vuetify.breakpoint.lgAndUp,'pa-2 subtitle-1': _vm.$vuetify.breakpoint.mdOnly, 'pa-1 body-2': _vm.$vuetify.breakpoint.smAndDown}},[_c('div',{staticClass:\"font-weight-medium\",class:{'display-1': _vm.$vuetify.breakpoint.lgAndUp,'headline': _vm.$vuetify.breakpoint.mdOnly, 'subheading': _vm.$vuetify.breakpoint.smAndDown}},[_c('span',{staticStyle:{\"font-family\":\"Oswald\"}},[_vm._v(\" Spring Mass System\")])]),_c('div',{ref:\"ia\",staticStyle:{\"margin-top\":\"20px\"}}),_vm._v(\"\\n A spring-mass system is a mechanical system composed of a mass (or several masses) connected to a spring.The spring is used to provide a restoring force that acts on the mass when it is displaced from its equilibrium position.Spring-mass systems are commonly used in many engineering applications, such as suspension systems in vehicles, shock absorbers, and vibration isolators.\\n \"),_c('div',{ref:\"ib\",staticStyle:{\"margin-top\":\"20px\"}}),_c('div',{staticClass:\"font-weight-medium\",class:{'display-1': _vm.$vuetify.breakpoint.lgAndUp,'headline': _vm.$vuetify.breakpoint.mdOnly, 'subheading': _vm.$vuetify.breakpoint.smAndDown}},[_c('span',{staticStyle:{\"font-family\":\"Oswald\"}},[_vm._v(\" Oscillations of Spring Mass System\")])]),_c('div',{ref:\"ib\",staticStyle:{\"margin-top\":\"20px\"}}),_vm._v(\"\\n From the definition of Simple Harmonic Motion, the force acting on the body executing it is:\\n $$ F=-kx $$\\n where \\\\(k\\\\) is the spring constant of the spring.\\n Using Newton's second law, force can be expressed in terms of mass \\\\(m\\\\) and acceleration \\\\(a\\\\).\\n $$F = m a = m \\\\frac{d^2x}{dt^2}$$\\n \"),_c('br'),_vm._v(\"\\n Substituting this in original equation, we obtain —\\n $$\\\\frac{d^2 x}{dt^2}=-\\\\frac{k}{m}x $$\\n This is the governing different equation for oscillations of a spring-mass system.\\n The general solution for the above equation is of the form:\\n $$x= A \\\\sin(\\\\omega t + \\\\phi)$$\\n Here \\\\(A\\\\) is the amplitude of the oscillations, \\\\(\\\\phi\\\\) is called the phase constant, and \\\\(\\\\omega\\\\) is called the angular frequency of the oscillations.\\n \"),_c('br'),_vm._v(\" Given the position, we can easily obtain the other parameters like velocity and acceleration. Taking the first derivative gives —\\n $$\\\\frac{dx}{dt}=A\\\\omega \\\\cos(\\\\omega t+\\\\phi)$$\\n Taking the second derivative gives —\\n $$\\\\frac{d^2x}{dt^2}=-A\\\\omega^2 \\\\sin(\\\\omega t+\\\\phi)$$\\n Substituting this in the governing differential equation, we obtain —\\n $$ - A\\\\omega^2 \\\\sin(\\\\omega t+\\\\phi) = - \\\\frac{k}{m} A \\\\sin(\\\\omega t+\\\\phi)$$\\n Upon simplifying we obtain —\\n $$\\\\omega^2 = \\\\frac{k}{m}$$\\n Or, equivalently\\n $$ \\\\omega = \\\\sqrt{\\\\frac{k}{m}}$$\\n \"),_c('div',{ref:\"ib\",staticStyle:{\"margin-top\":\"20px\"}}),_c('div',{staticClass:\"font-weight-medium\",class:{'display-1': _vm.$vuetify.breakpoint.lgAndUp,'headline': _vm.$vuetify.breakpoint.mdOnly, 'subheading': _vm.$vuetify.breakpoint.smAndDown}},[_c('span',{staticStyle:{\"font-family\":\"Oswald\"}},[_vm._v(\" Frequency & Time Period of Oscillations\")])]),_c('div',{ref:\"ic\",staticStyle:{\"margin-top\":\"20px\"}}),_vm._v(\"\\n The time period of simple harmonic motion is related to angular frequency as:\\n $$T=\\\\frac{2\\\\pi}{\\\\omega}$$\\n Substituting for \\\\(\\\\omega\\\\) we obtain —\\n $$T = 2\\\\pi \\\\sqrt{\\\\frac{m}{k}}$$\\n \"),_c('div',{ref:\"id\",staticStyle:{\"margin-top\":\"20px\"}}),_c('div',{staticClass:\"font-weight-medium\",class:{'display-1': _vm.$vuetify.breakpoint.lgAndUp,'headline': _vm.$vuetify.breakpoint.mdOnly, 'subheading': _vm.$vuetify.breakpoint.smAndDown}},[_c('span',{staticStyle:{\"font-family\":\"Oswald\"}},[_vm._v(\" Learn Interactively | Spring-Mass System\")])]),_c('div',{ref:\"ie\",staticStyle:{\"margin-top\":\"20px\"}}),_vm._v(\"\\n You are shown a spring-mass system. Select mass of the block and spring constant. Drag the mass down and then let go to see the oscillations of the block.\\n \")]),_c('v-responsive',[_c('v-layout',{attrs:{\"justify-center\":\"\"}},[_c('div',{staticClass:\"edliy-box-about\",attrs:{\"id\":\"jxgbox1\"}})]),_c('v-layout',{attrs:{\"justify-center\":\"\"}},[_c('h5',{staticClass:\"edliy-text-about\"},[_vm._v(\"\\n Select mass of the block and spring constant. Drag the mass down and then let go to see the oscillations of the block.\\n \")])])],1)],1)\n}\nvar staticRenderFns = []\n\nexport { render, staticRenderFns }","import {\r\n makeResponsive,\r\n //makeResponsive(brd1);\r\n placeTitle,\r\n //placeTitle(brd1,'title', 'subtitle');\r\n placeImage,\r\n placeInput,\r\n placeSlider,\r\n hoverMe,\r\n placeRec,\r\n hiddenPt,\r\n fixedPt,\r\n clearInputFields,\r\n dragMe,\r\n placeArrow,\r\n //placeArrow(board, pt1, pt2, width, cols)\r\n placeGravity,\r\n placeText,\r\n //placeText(board, positionX, positionY, message)\r\n placeLine,\r\n placePoint,\r\n placeGlider,\r\n placeRuler,\r\n placeLeftText,\r\n placeSliderSwitch,\r\n placeBoldText,\r\n //placeBoldText(brd6, -9, 1, 'Liquid');\r\n placeDash,\r\n // placeDash(board, [x1, y1], [x2, y2], width, cols)\r\n writeRightText,\r\n writeLeftText,\r\n placeLabel,\r\n placeLogo,\r\n placeShuffle,\r\n toggle,\r\n writeHTMLText,\r\n alert,\r\n writeMiddleText,\r\n placeStartOver,\r\n drawSegment,\r\n drawPoint\r\n} from '../Utils';\r\nconst Boxes = {\r\n box1: function () {\r\n var board = JXG.JSXGraph.initBoard('jxgbox1', {boundingbox: [-6, 10, 9, -5], keepaspectratio: true, axis:false, grid:true, ticks:false, showCopyright:false, showNavigation:false, pan:{enabled:false}, zoom:{enabled:false}});\r\n //\r\n board.options.board.minimizeReflow = 'none';\r\n board.options.text.highlight=false;\r\n board.options.text.fixed=true;\r\n board.options.image.highlight=false;\r\n board.options.text.cssDefaultStyle='fontFamily:Oswald';\r\n board.options.line.highlight=false;\r\n board.options.curve.highlight=false;\r\n board.options.point.highlight=false;\r\n board.options.point.showInfoBox=false;\r\n //\r\n board.options.layer['image'] =10;\r\n //\r\n makeResponsive(board);\r\n placeLogo(board);\r\n placeTitle(board, 'Spring Mass System', '(Drag the mass down. Then let go)');\r\n //\r\n let xAxis =board.create('axis', [[0, 0],[5, 0]], { strokeColor:'grey',\r\n highlight:false, strokeWidth: ()=>Math.round(2*board.canvasWidth/800.),\r\n withLabel:true, name: '', straightFirst:false, straightLast:true, lastArrow:false,\r\n label: {\r\n display:'internal',\r\n fontSize:function(){return 24*board.canvasHeight/800},\r\n CssStyle: 'fontFamily:Oswald;fontWeight:bold',\r\n position: 'rt',\r\n offset: [-20, 20]}});\r\n\r\n //\r\n let yAxis =board.create('axis', [[0, -5],[0, 8]], { strokeColor:'grey',\r\n highlight:false, strokeWidth: ()=>Math.round(2*board.canvasWidth/800.),\r\n withLabel:true, name: '', straightFirst:false, straightLast:false, lastArrow:false,\r\n label: {\r\n display:'internal',\r\n fontSize:function(){return 24*board.canvasHeight/800},\r\n CssStyle: 'fontFamily:Oswald;fontWeight:bold',\r\n position: 'rt',\r\n offset: [-20, 20]}});\r\n var line = board.create('line', [[-2.5,8], [-2.5, -8]], {visible: false, straightFirst: false, straightLast: false});\r\n //\r\n var point = board.create('glider', [-2.5, 0, line], {name: '', size:function(){return 45*board.canvasHeight/800}, face:'square'});\r\n //\r\n var ktext= board.create('text',[-1.5, function(){return (5+point.Y())/2.0}, 'k'],{display:'internal', cssStyle:'fontFamily:Oswald',fontSize:function(){return Math.round(16*board.canvasWidth/500.)}, fixed:true});\r\n //\r\n var mtext= board.create('text',[-2.5, function(){return point.Y()}, 'm'],{display:'internal', anchorX:'middle', cssStyle:'fontFamily:Oswald',fontSize:function(){return Math.round(16*board.canvasWidth/500.)}, fixed:true});\r\n //\r\n var Ltext= board.create('text',[-5, 2.5, 'L_o'],{display:'html', anchorX:'middle', cssStyle:'fontFamily:Oswald',fontSize:function(){return Math.round(16*board.canvasWidth/500.)}, fixed:true});\r\n //\r\n var msg1 =writeMiddleText(board, 4.5, 6.5, 'Max weight reached!');\r\n msg1.setAttribute({color:'red', visible:false});\r\n //\r\n var msg2 =writeMiddleText(board, 4.5, 6.5, 'Min weight reached!');\r\n msg2.setAttribute({color:'red', visible:false});\r\n //\r\n var m=0.25;\r\n var add = board.create('image', ['/assets/plus.svg', [-5., 7-0.375], [0.75, 0.75]],{fixed:true});\r\n var remove = board.create('image', ['/assets/minuss.svg', [-1.75, 7-0.375], [0.75, 0.75]],{fixed:true});\r\n //\r\n add.on('down',function(){if(m<4*0.25){m+=1*0.25}else{m=4*0.25; alert(board, msg1)}; point.moveTo([-2.5, 0.0]);board.stopAllAnimation(); Pt0.moveTo([0, ()=>point.Y()]); vis=false, viss=false});\r\n remove.on('down',function(){if(m>1*0.25){m-=1*0.25;}else{m=1*0.25; alert(board, msg2)}; point.moveTo([-2.5, 0.0]);board.stopAllAnimation(); Pt0.moveTo([0, ()=>point.Y()]); vis=false, viss=false});\r\n //\r\n var k=1;\r\n var addK = board.create('image', ['/assets/plus.svg', [-5., 6-0.375], [0.75, 0.75]],{fixed:true});\r\n var removeK = board.create('image', ['/assets/minuss.svg', [-1.75,6-0.375], [0.75, 0.75]],{fixed:true});\r\n addK.on('down',function(){if(k<4){k+=1}else{k=4; alert(board, msg1)};point.moveTo([-2.5, 0.0]);board.stopAllAnimation(); Pt0.moveTo([0, ()=>point.Y()]); vis=false, viss=false});\r\n removeK.on('down',function(){if(k>1){k-=1;}else{k=1; alert(board, msg2)}; point.moveTo([-2.5, 0.0]);board.stopAllAnimation(); Pt0.moveTo([0, ()=>point.Y()]); vis=false, viss=false});\r\n //\r\n board.create('text',[-3., 7, ()=>'m = '+m.valueOf()+' kg'],{display:'internal', anchorX:'middle', color:'red', cssStyle:'fontFamily:Oswald',fontSize:function(){return Math.round(16*board.canvasWidth/500.)}, fixed:true});\r\n//\r\n board.create('text',[-3., 6, ()=>'k = '+k.valueOf()+' N/m'],{display:'internal', anchorX:'middle', color:'blue', cssStyle:'fontFamily:Oswald',fontSize:function(){return Math.round(16*board.canvasWidth/500.)}, fixed:true});\r\n //\r\n var isInDragMode = false;\r\n //\r\n var springHangup = board.create('point', [0, 0], {color: 'black', name: '', fixed: true, visible:false});\r\n //\r\n var i=0;\r\n var numberOfSpringRings = 50;\r\n var springRings = [];\r\n //\r\n for(i=0; i0)\r\n board.create('segment', [springRings[i-1], springRings[i]], {color:'blue', strokeWidth:()=>2*board.canvasWidth/800});\r\n };\r\n //\r\n //\r\n var vbase=board.create('polygon',[[-6,5],[-0.,5],[-0.,8],[-6, 8]], {fillColor:'lightgrey', fillOpacity:0.6, withLines:false, vertices:{visible:false}});\r\n // board.create('segment', [springHangup, springRings[0]], {color: 'black', strokeWidth: 1});\r\n board.create('point', [-4.5, 0.1], {name: '', color:'grey', size:function(){return 4*board.canvasHeight/800}, face:'triangledown'});\r\n//\r\n board.create('point', [-4.5, 4.9], {name: '', color:'grey', size:function(){return 4*board.canvasHeight/800}, face:'triangleup', fixed:true});\r\n //\r\n board.create('segment', [[-4.5, 0],[-4.5, 5] ], {fixed:true, strokeColor:'black', strokeWidth:1});\r\n //\r\n function startAnimation(startY) {\r\n point.moveAlong(function(){\r\n let dt = 1000;\r\n let duration = 10*dt*2*Math.PI*m.valueOf()/k.valueOf();\r\n return function(t) {\r\n if (t >= duration){\r\n //a=0;\r\n return [0, 0];\r\n }\r\n else {\r\n a= startY;\r\n return [-2.5, startY*Math.cos((k.valueOf()/m.valueOf())*t/dt)]\r\n }\r\n }}()\r\n );}\r\n var a =0; var vis=false;\r\n var Pt0 = board.create('point', [0, 0], {name: '', color:'black',visible:()=>vis==true||viss==true, size:function(){return 5*board.canvasHeight/800}, face:'triangleleft'});\r\n //\r\n function startPlotting(startY) {\r\n Pt0.moveAlong(function(){\r\n let dt = 1000;\r\n let duration = 10*dt*2*Math.PI*m.valueOf()/k.valueOf();\r\n let half = 9*dt*Math.sqrt(m.valueOf()/k.valueOf());\r\n let secondhalf= 18*dt*Math.sqrt(m.valueOf()/k.valueOf());\r\n return function(t) {\r\n if (t >= duration){\r\n viss=true;\r\n // a=0;\r\n // return [0, 0];\r\n }\r\n else if (t>=half){\r\n viss=true;\r\n vis = false\r\n return [t/dt/(Math.sqrt(m.valueOf()/k.valueOf()))-9, startY*Math.cos((k.valueOf()/m.valueOf())*t/dt)]\r\n }\r\n else {\r\n a= startY;\r\n vis=true;\r\n viss=false;\r\n return [t/dt/(Math.sqrt(m.valueOf()/k.valueOf())), startY*Math.cos((k.valueOf()/m.valueOf())*t/dt)]\r\n }\r\n }}()\r\n);}\r\n//\r\n let Pt1 = board.create('point', [0+0.1, ()=>-1.25*Math.abs(a)], {name: '', color:'black',visible:()=>vis==true||viss==true, size:function(){return 4*board.canvasHeight/800}, face:'triangleleft'});\r\n//\r\n board.create('text',[()=>Math.PI*2*Math.sqrt(m.valueOf()/k.valueOf())/2, ()=>-1.4*Math.abs(a), ()=>'T = '+Math.min(Pt0.X(), Math.PI*2*Math.sqrt(m.valueOf()/k.valueOf())).toFixed(2)+' sec'],{visible:()=>vis==true||viss==true, display:'internal',\r\n anchorY:'top', anchorX:'middle', cssStyle:'fontFamily:Oswald',fontSize:function(){return Math.round(12*board.canvasWidth/500.)}, fixed:true});\r\n//\r\n let Pt2 =board.create('point', [()=>Math.min(Pt0.X(), Math.PI*2*Math.sqrt(m.valueOf()/k.valueOf())), ()=>-1.25*Math.abs(a)], {name: '', visible:()=>vis==true||viss==true, color:'black', size:function(){return 4*board.canvasHeight/800}, face:'triangleright', fixed:true});\r\n//\r\n var viss=false;\r\n var plot = board.create('functiongraph', [function(x){return a*Math.cos(Math.sqrt(k.valueOf()/m.valueOf())*x)}, 0, ()=>Pt0.X()],{visible:()=>vis==true,strokeColor:'grey', strokeWidth:()=>3*board.canvasWidth/800});\r\n board.create('functiongraph', [function(x){return a*Math.cos(Math.sqrt(k.valueOf()/m.valueOf())*(x+9))}, 0, ()=>Pt0.X()],{visible:()=>viss==true,strokeColor:'grey', strokeWidth:()=>3*board.canvasWidth/800});\r\n//\r\n var Pt3=drawPoint(board, -3.5, 0).setAttribute({visible:false});\r\n var Pt4=drawPoint(board, -5.5, 0).setAttribute({visible:false});\r\n//\r\n drawSegment(board, Pt3, Pt4).setAttribute({strokeColor:'grey'});\r\n//\r\n drawSegment(board, Pt1, Pt2).setAttribute({visible:()=>vis==true||viss==true});\r\n//\r\n// add.on('down', function(){return board.stopAllAnimation();point.moveTo([-2.5,0])});\r\n// k.on('down', function(){return board.stopAllAnimation(); point.moveTo([-2.5, 0])});\r\n function hook() {\r\n if(!isInDragMode) {\r\n if(board.mode === board.BOARD_MODE_DRAG) {\r\n isInDragMode = true;\r\n board.stopAllAnimation(); }\r\n }\r\n if(isInDragMode) {\r\n if(board.mode !== board.BOARD_MODE_DRAG) {\r\n isInDragMode = false;\r\n startAnimation(point.Y());\r\n startPlotting(point.Y());\r\n }\r\n }\r\n }\r\n board.addHook(hook);\r\n},\r\n}\r\nexport default Boxes;\r\n","\r\n\r\n","import mod from \"-!../../../../../node_modules/cache-loader/dist/cjs.js??ref--12-0!../../../../../node_modules/thread-loader/dist/cjs.js!../../../../../node_modules/babel-loader/lib/index.js!../../../../../node_modules/cache-loader/dist/cjs.js??ref--0-0!../../../../../node_modules/vue-loader/lib/index.js??vue-loader-options!./Spring.vue?vue&type=script&lang=js&\"; export default mod; export * from \"-!../../../../../node_modules/cache-loader/dist/cjs.js??ref--12-0!../../../../../node_modules/thread-loader/dist/cjs.js!../../../../../node_modules/babel-loader/lib/index.js!../../../../../node_modules/cache-loader/dist/cjs.js??ref--0-0!../../../../../node_modules/vue-loader/lib/index.js??vue-loader-options!./Spring.vue?vue&type=script&lang=js&\"","import { render, staticRenderFns } from \"./Spring.vue?vue&type=template&id=6b8575f0&\"\nimport script from \"./Spring.vue?vue&type=script&lang=js&\"\nexport * from \"./Spring.vue?vue&type=script&lang=js&\"\n\n\n/* normalize component */\nimport normalizer from \"!../../../../../node_modules/vue-loader/lib/runtime/componentNormalizer.js\"\nvar component = normalizer(\n script,\n render,\n staticRenderFns,\n false,\n null,\n null,\n null\n \n)\n\nexport default component.exports"],"sourceRoot":""}