$(A)$ Restoring force is directly proportional to the displacement.
$(B)$ The acceleration and displacement are opposite in direction.
$(C)$ The velocity is maximum at mean position.
$(D)$ The acceleration is minimum at extreme points.
Choose the correct answer from the options given below :
$a=-\omega^2 x B \text { true }$
$\text { Velocity is maximum at mean position } C \text { true }$
$\text { Acceleration is maximum at extreme } D \text { false }$
$\text { points }$
$(A)$ the speed of the particle when it returns to its equilibrium position is $u_0$.
$(B)$ the time at which the particle passes through the equilibrium position for the first time is $t=\pi \sqrt{\frac{ m }{ k }}$.
$(C)$ the time at which the maximum compression of the spring occurs is $t =\frac{4 \pi}{3} \sqrt{\frac{ m }{ k }}$.
$(D)$ the time at which the particle passes througout the equilibrium position for the second time is $t=\frac{5 \pi}{3} \sqrt{\frac{ m }{ k }}$.


