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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




Question Number 32757 by NECx last updated on 01/Apr/18
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)calculate the time interval from  t=0 before the displacement is  0.08m
Amassoscillatingonaspringhasamplitudeof1.2mandaperiodof2s.Deducetheequationforthedisplacementxifthetimingstartsattheinstantwhenthemasdhasitsmaximumdisplacement.b)calculatethetimeintervalfromt=0beforethedisplacementis0.08m
Commented by NECx last updated on 01/Apr/18
This was what I did    x=Acos ωt  (dx/dt)=−Aωsin wt  at the maximum displacement  dx/dt=0  ∴ 0=−Awsinwt  sinwt=0  wt=0,π,2π,..........  since w=2π/T  then w=π  ∵t={0,1,2,........}s    ∵x=1.2cos0        when t=0    x=1.2cosπ      when t=1    and so on.....   This doesnt seem to me like the  right answer so I′m confused.
ThiswaswhatIdidx=Acosωtdxdt=Aωsinwtatthemaximumdisplacementdx/dt=00=Awsinwtsinwt=0wt=0,π,2π,.sincew=2π/Tthenw=πt={0,1,2,..}sx=1.2cos0whent=0x=1.2cosπwhent=1andsoon..ThisdoesntseemtomeliketherightanswersoImconfused.
Commented by NECx last updated on 02/Apr/18
someone please help.Please I′ve  been struggling with it for a long while
someonepleasehelp.PleaseIvebeenstrugglingwithitforalongwhile
Commented by NECx last updated on 02/Apr/18
I think Mrw2 and Ajfour   have not been online.  Really obvious.
IthinkMrw2andAjfourhavenotbeenonline.Reallyobvious.
Commented by float last updated on 03/Apr/18
Amplitude A=1.2 m  Period T=2 s  ∴ ω=((2π)/T)=((2π)/(2 s))=π Hz  Therefore, x(t)=A cos(ωt)=1.2∙cos(πt).  b) x(t)=1.2∙cos(πt)=0.08 m  ∴ t=((arccos(((0.08)/(1.2))))/π)≈0.48 s
AmplitudeA=1.2mPeriodT=2sω=2πT=2π2s=πHzTherefore,x(t)=Acos(ωt)=1.2cos(πt).b)x(t)=1.2cos(πt)=0.08mt=arccos(0.081.2)π0.48s
Commented by NECx last updated on 03/Apr/18
thanks... what if we′re asked to  find the velocity at this instant??
thankswhatifwereaskedtofindthevelocityatthisinstant??
Answered by tanmay.chaudhury50@gmail.com last updated on 20/May/18
x=Acos(((2Π)/T)t+θ)   given A=1.2m   T=2sec  when t=0 x=A  A=Acos(((2Π)/T)×0+θ)  cosθ=1  θ=0  x=Acos(((2Π)/T)t)  cos(((2Π)/T)t)=(x/A)  t=(T/(2Π))cos^(−1) ((x/A))  t=(2/(2×3.14))cos^(−1) (((0.08)/(1.2)))
x=Acos(2ΠTt+θ)givenA=1.2mT=2secwhent=0x=AA=Acos(2ΠT×0+θ)cosθ=1θ=0x=Acos(2ΠTt)cos(2ΠTt)=xAt=T2Πcos1(xA)t=22×3.14cos1(0.081.2)

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