A-mass-oscillating-on-a-spring-has-amplitude-of-1-2m-and-a-period-of-2s-Deduce-the-equation-for-the-displacement-x-if-the-timing-starts-at-the-instant-when-the-masd-has-its-maximum-displacement-b-cal

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Question Number 32757 by NECx last updated on 01/Apr/18

$$Amassoscillatingonaspring$$$$hasamplitudeof1.2mandaperiod$$$$of2s.Deducetheequationfor$$$$thedisplacementxifthetiming$$$$startsattheinstantwhenthemasd$$$$hasitsmaximumdisplacement.$$$$b)calculatethetimeintervalfrom$$$$t=0beforethedisplacementis$$$$0.08m$$$$$$

Commented by NECx last updated on 01/Apr/18

$$ThiswaswhatIdid$$$$$$$$x=A\cos \omega t$$$$\frac{dx}{dt}=-A\omega \sin wt$$$$atthemaximumdisplacement$$$$dx/dt=0$$$$\therefore 0=-Awsinwt$$$$sinwt=0$$$$wt=0,\pi ,2\pi ,\dots \dots \dots .$$$$sincew=2\pi /T$$$$thenw=\pi$$$$\because t=\{0,1,2,\dots \dots ..\}s$$$$$$$$\because x=1.2cos0whent=0$$$$$$$$x=1.2cos\pi whent=1$$$$$$$$andsoon\dots ..$$$$Thisdoesntseemtomelikethe$$$$rightanswerso{I}^{\prime }mconfused.$$

Commented by NECx last updated on 02/Apr/18

$$someonepleasehelp.Please{I}^{\prime }ve$$$$beenstrugglingwithitforalongwhile$$

Commented by NECx last updated on 02/Apr/18

$$IthinkMrw2andAjfour$$$$havenotbeenonline.$$$$Reallyobvious.$$

Commented by float last updated on 03/Apr/18

$$\mathrm{Amplitude}A=1.2\mathrm{m}$$$$\mathrm{Period}T=2\mathrm{s}$$$$\therefore \omega =\frac{2\pi }{T}=\frac{2\pi }{2s}=\pi \mathrm{Hz}$$$$\mathrm{Therefore},x\left(t\right)=A\cos \left(\omega t\right)=1.2\cdot \cos \left(\pi t\right).$$$$\mathrm{b})x\left(t\right)=1.2\cdot \cos \left(\pi t\right)=0.08\mathrm{m}$$$$\therefore t=\frac{\arccos \left(\frac{0.08}{1.2}\right)}{\pi }\approx 0.48\mathrm{s}$$

Commented by NECx last updated on 03/Apr/18

$$thanks\dots whatif{we}^{\prime }reaskedto$$$$findthevelocityatthisinstant??$$

Answered by tanmay.chaudhury50@gmail.com last updated on 20/May/18

$$x=Acos(\frac{2\mathrm{\Pi }}{T}t+\theta )givenA=1.2mT=2sec$$$$whent=0x=A$$$$A=Acos(\frac{2\mathrm{\Pi }}{T}\times 0+\theta )$$$$cos\theta =1$$$$\theta =0$$$$x=Acos\left(\frac{2\mathrm{\Pi }}{T}t\right)$$$$cos\left(\frac{2\mathrm{\Pi }}{T}t\right)=\frac{x}{A}$$$$t=\frac{T}{2\mathrm{\Pi }}{cos}^{-1}\left(\frac{x}{A}\right)$$$$t=\frac{2}{2\times 3.14}{cos}^{-1}\left(\frac{0.08}{1.2}\right)$$

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