SHM10

1.2.4 Acceleration

From v = vo cos ω t = x0 ω cos ω t

where xo is the maximum displacement

differentiating we get

$a=\frac{dv}{dt}=-{\omega }^{2}\left({x}_{0}sin\omega t\right)=-{\omega }^{2}x$
Variation with time of acceleration

In terms of x:

Therefore,  a = - xo ω2 sin ω t
= - ω2 (xo sin ω t)
which is the defining equation for S.H.M. !
a     = - ω2 x

Variation with displacement of acceleration

since

a = – a0sin ω t

where ao is the maximum acceleration
where by a0 = ω2 (xo)

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end faq

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