Question

The position x of particle moving along x axis varies with time as x=Asin(wt) where A n w are contant. The acc of particle varies with its position x as

Answer 1

The position x of particle moving along x -axis varies with time as $x=Asin\omega t$....(1)

differentiate x with respect to time to find velocity of particle at any instant t.
e.g., $\frac{dx}{dt}=v=\omega Acos\omega t$
we know, acceleration is the rate of change of velocity per unit time.
so, differentiate v with respect to time to find Acceleration of particle at any instant t,

$\frac{dv}{dt}=-\omega^2Asin\omega t$

from equation (1),

$a=-\omega^2x$

Answer 2

Answer:a= -w^2x

Explanation: x= Asin(wt)

Or, dx/dt= wAcos(wt)

Or, v= wAcos(wt)

Now, dv/dt= - w^2 Asin(wt)

Or, a= - w^2 x