D. C. Pandey Solutions for Chapter: Simple Harmonic Motion, Exercise 1: Objective Problems

A particle is moving with constant angular velocity along the circumference of a circle. Which of the following statements is true?

Which of the following is a necessary and sufficient condition for $\mathrm{SHM}$?

The displacement $x$ (in metre) of a particle in simple harmonic motion is related to time $t$ (in second) as $x=0.01\cos \left(\pi t+\frac{\pi }{4}\right)$. The frequency of the motion will be,

In a simple pendulum, the period of oscillation $T$ is related to length of the pendulum $l$ as,

The ratio of frequencies of two pendulums are $2:3$, then their lengths are in ratio

The maximum acceleration of a particle in $\mathrm{SHM}$ is made two times keeping the maximum speed to be constant. It is possible when

A metal rod of length $L$ and mass $m$ is pivoted at one end. A thin disc of mass $M$ and radius $R\left(<L\right)$ is attached at its centre to the free end of the rod. Consider two ways the disc is attached.
Case A -the disc is not free to rotate about its centre.
Case B-the disc is free to rotate about its centre. The rod disc system performs $\mathrm{SHM}$ in vertical plane after being released from the same displaced position.
Which of the following statement(s) is/are correct?

A wooden cube (density of wood $d$) of side $l$ floats in a liquid of density $\mathrm{\rho }$ with its upper and lower surfaces horizontal. If the cube is pushed slightly down and released, it performs simple harmonic motion of period $T$ then $T$ is equal to