Question

The position x of a particle moving along x axis varies with time t as x = Asin(wt) , where A and w are constants . The acceleration of the particle varies with its position as
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Answer 1

Let's see

$\\ \rm\Rrightarrow x=Asin(\omega t)\dots(1)$

Now we know the formula of acceleration

$\\ \rm\Rrightarrow \alpha=-A\omega^2sin(\omega t)$

$\\ \rm\Rrightarrow \alpha=-Asin(\omega t)\times \omega^2$

• From eq(1)

$\\ \rm\Rrightarrow \alpha=-x\omega^2$

Or

$\\ \rm\Rrightarrow \alpha=-\omega^2x$

Answer 2

$\sf{x= Asin(wt)}$

$\sf{Or, \frac{dx}{dt}= wAcos(wt)}$

$\sf{Or, v= wAcos(wt)}$

Now,

$\sf{\frac{dv}{dt} = - w^2 Asin(wt)}$

$\sf{Or, a=- w^2 x}$