$A$ simple harmonic motion having an amplitude $A$ and time period $T$ is represented by the equation: $y = 5 \sin \pi (t + 4) \ m$. Then the values of $A$ (in $m$) and $T$ (in $sec$) are:

$A$ particle is executing simple harmonic motion with an instantaneous displacement $x = A \sin^2(\omega t - \frac{\pi}{4})$. The time period of oscillation of the particle is

$A$ system exhibiting $S.H.M.$ must possess

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:

The figure depicts four $x-t$ plots for the linear motion of a particle. Which of the plots represent periodic motion? What is the period of motion (in case of periodic motion)?

What is the importance of periodic $\text{sine}$ and $\text{cosine}$ functions in physics?