K K Sharma Solutions for Chapter: Oscillations, Exercise 1: TOPICWISE QUESTIONS

A uniform square plate of side $a$ is hinged at one of its corners. It is suspended such that it can rotate about horizontal axis lying in its plane and passing through its center. Find out its time period of small oscillation about its equilibrium position. 

A meter stick swinging in vertical plane about a fixed horizontal axis passing through its one end undergoes small oscillation of frequency $f_0$. If the bottom half of the stick was cut off, then its new frequency of small oscillation will be?

Pendulum $A$ is a physical pendulum made up of thin rigid and uniform rod whose length is $L$. One end of this rod is attached to the ceiling by a frictionless hinge so that rod is free to swing back and forth. Pendulum $B$is a simple pendulum whose length is also $L$. The ratio $\frac{{{\rm T}}_A}{T_B}$ for small angular oscillations is 

The position of a particle with respect to origin varies according to the relation $x=3\sin 100t+8{\cos }^{2}50t$. Which of the following is correct about this motion?

A particle is subjected to two simple harmonic motions along $x$ and $y$ directions according to $x=3\sin 100\pi t$ and $y=4\sin 100\pi t$. Then mark the correct statement among the following.

The resultant of two simple harmonic motions of the same frequency and unequal amplitudes but differing in phase by, $\frac{\mathrm{\pi }}{2}$ is 

The motion of a particle is given, $x=A\sin \omega t+B\cos \omega t$. The motion of the particle is

A $20 \mathrm{g}$ particle is subjected to two simple harmonic motions $x_1=2 \sin 10t$, $x_2=4 \sin (10t+\frac{\pi }{3})$ where $x_1$ and $x_2$ are in meter and $t$ is in second. Then, choose the incorrect option.