$A$ particle is oscillating according to the equation $X = 7 \cos(0.5 \pi t)$,where $t$ is in seconds. The particle moves from the position of equilibrium to maximum displacement in time ..... $s$.

The figure shows the $x-t$ plot of a particle executing one-dimensional simple harmonic motion. Determine the signs of the position,velocity,and acceleration variables of the particle at $t = 0.3 \; s$,$t = 1.2 \; s$,and $t = -1.2 \; s$.

Which of the following equations does not represent a simple harmonic motion?

$A$ particle of mass $m$ is under the influence of a force $F = (-kx + F_0) \text{ N}$. The particle,when disturbed,will oscillate

One end of a rod of length $L$ is fixed to a point on the circumference of a wheel of radius $R$. The other end is sliding freely along a straight channel passing through the centre of the wheel as shown in the figure below. The wheel is rotating with a constant angular velocity $\omega$ about $O$. Taking $T = \frac{2 \pi}{\omega}$,the motion of the rod is

In a linear simple harmonic motion $(SHM)$:
$(A)$ Restoring force is directly proportional to the displacement.
$(B)$ The acceleration and displacement are opposite in direction.
$(C)$ The velocity is maximum at the mean position.
$(D)$ The acceleration is minimum at extreme points.
Choose the correct answer from the options given below: