Embibe Experts Solutions for Chapter: Simple Harmonic Motion, Exercise 1: TS EAMCET 2020 (28-Sep Shift-1)

The function $(\sin \omega t-\cos \omega t)$ represents the S.H.M having a time period $T$

An object was found to make oscillations governed by the equation $y={\cos }^2\left(\omega t+\frac{\pi }{4}\right)-0.5$. The amplitude and angular frequency of these oscillations, respectively, are

A hollow sphere of radius $R$ is suspended from a thin rod. If the sphere is twisted by a small angle about the wire axis and released, simple harmonic oscillation (SHM) will ensure with a period of ${\tau }_1$. Now, if the hollow sphere is replaced by a solid sphere of radius and mass equal to that of a hollow sphere, the SHM will have a period ${\tau }_2$. The ratio of time periods $\left({\tau }_1/{\tau }_2\right)$ 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

An oscillating simple pendulum slow down its motion and finally stops due to?

Two simple pendulums with time periods $T_0$ and $T_1$ start oscillating in the same direction at the same time. If $T_0>T_1$ and the phase difference between them is $\frac{\pi }{3}$ when the faster pendulum has completed one oscillation, then $T_1$ is

A cylindrical block of wood of mass $10 \mathrm{kg}$ and radius $10 \mathrm{cm}$ is floating in water with its axis vertical. When it is depressed a little and then released, it starts executing simple hormonic motion (SHM). The frequency of the SHM, executed by the block is:
(Assume $g=10 \mathrm{m} {\mathrm{s}}^{-2}$ and let $\rho$ is the density of the water)