The oscillations represented by curve $1$ in the graph are expressed by equation $x=A\sin \omega t$. The equation for the oscillations represented by curve $2$ is expressed as:

 

A $4 \mathrm{kg}$ particle is moving along the$x$-axis under the action of the force $F=-\left(\frac{{\pi }^2}{16}\right)x \mathrm{N}$ . At $t=2 \sec$, the particle passes through the origin and at $t=10 \sec$ its speed is $4\sqrt{2} \mathrm{m} {\mathrm{s}}^{-1}$. The amplitude of the motion is:

Graph shows the$x \left(t\right)$ curves for three experiments involving a particular spring-block system oscillating in SHM. The kinetic energy of the system is largest at $t=4 \mathrm{s}$ for the situation:

The acceleration of a particle moving along $x$-axis is given by $a=-100x+50$. It is released from $x=0$. Here, $a$ and $x$ are in SI units. The motion of particle will be:

A particle performs S.H.M. of amplitude $A$ along a straight line. When it is at a distance $\frac{\sqrt{3}}{2} \mathrm{A}$ from mean position, its kinetic energy gets increased by an amount $\frac{1}{2}m{\omega }^2{A}^2$ due to an impulsive force.

Then its new amplitude becomes: