Exercise 1

Assertion (A): In a periodic motion, the particle repeats the motion with same parameters of motion.

Reason (R): For a particle performing periodic motion, there must be a net force acting on the particle at every instant of motion.

The energy of a particle executing simple harmonic is given by $E=a{x}^2+b{v}^2$, where $x$ is the displacement from mean position $x=0$ and $v$ is the velocity of the particle at $x$ then choose the incorrect statement.

A horizontal spring-block system of mass $2 \mathrm{kg}$ executes $\mathrm{S}.\mathrm{H}.\mathrm{M}.$ When the block is passing through its equilibrium position, an object of mass $1 \mathrm{kg}$ is put gently on it and the two move together. The new amplitude of vibration is ($A$ being its initial amplitude):

A block of mass $\text{'}m\text{'}$ is attached with two springs of spring constant $\text{'}k\text{'}$ is performing $\mathrm{SHM}$ on a smooth horizontal surface. One of the spring is cut when the block is at the extreme position. Find the ratio of the amplitude of new $\mathrm{SHM}$ and old $\mathrm{SHM}.$

The displacement of a particle is given by, $x={\cos }^2\omega t$. The motion is,

The displacement equations for two waves undergoing superposition are, respectively, $y_1=4\sin \omega t$ and $y_2=3\sin \left(\omega t+\frac{\pi }{2}\right)$. The amplitude of the resultant wave is,

Two clocks $A$ and $B$ are synchronized to show the same time on earth. Clock $A$ is based on oscillations of spring and clock $B$ is based on a pendulum motion. If these two clocks are taken to the surface of the moon, then

Two simple pendulums have the same period of oscillation. The necessary condition for this is