Answer to Question #93972 in Classical Mechanics for ayush meena
A particle of mass m is subject to a force f(X)= Kx. the initial position is 0 and the initial speed is V. Find x(t)
1
2019-09-09T11:06:47-0400
ma=mdt2d2x=Kx
x=eλt We have
λ2=mK→λ1=mK,λ2=−mK
x(t)=c1exp(mKt)+c2exp(−mKt)
x(0)=0=c1+c2→c1=−c2
v(t)=c1mK(exp(mKt)+exp(−mKt))
v(0)=v=c1mK(1+1) Thus,
x(t)=0.5vKm(exp(mKt)−exp(−mKt))
x(t)=vKmsh(mKt)
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