Embibe Experts Solutions for Chapter: Simple Harmonic Motion, Exercise 1: TS EAMCET - 5 August 2021 Shift 2

A particle is executing simple harmonic motion (S.H.M.). Its acceleration at a distance of $1 \mathrm{cm}$ from the mean position is $3 \mathrm{cm} {\mathrm{s}}^{-2}.$ If its velocity is $6 \mathrm{cm} {\mathrm{s}}^{-1}$ when it is at a distance of $2 \mathrm{cm}$ from its mean position, then the amplitude of S.H.M. is, 

A simple harmonic oscillator has an amplitude of $0.5 \mathrm{m}$ and a time period of $2$ seconds. What is the magnitude of acceleration when it is displaced from the mean position by $0.25 \mathrm{m}?$

A particle of mass $m$ is attached to four springs with spring constant $k,k,2k$ and $2k$ as shown in the figure. Four springs are attached to the four corners of a square and a particle is placed at the center. If the particle is pushed slightly towards any side of the square and released, the period of oscillation will be

The amplitude of the wave resulting from the superposition of three waves given by $x_1=A\cos \omega t, x_2=2A\sin \omega t$ and $x_3=\sqrt{2}A\cos \left(\omega t+\frac{\pi }{4}\right)$ is

A particle of mass $0.1 \mathrm{kg}$ is executing simple harmonic motion of amplitude $0.1 \mathrm{m}$. When the particle passes through the mean position, its kinetic energy is $8\times {10}^{-3} \mathrm{J}$. If the initial phase is $45°,$ the equation of its motion is (Assume, $x \left(t\right)$ as the position of the particle at time $t$)

Which of the following equation represents a simple harmonic motion? ($\omega$ is angular frequency, A is amplitude of oscillation and $i=\sqrt{-1}$)

A body of mass $1 \mathrm{kg}$ is executing simple harmonic motion (SHM). Its displacement $y$ (in $\mathrm{cm}$) at time t given by $y=\left[6\sin \left(100\mathrm{t}+\frac{\pi }{4}\right)\right]\mathrm{cm}.$ Its maximum kinetic energy is

The displacement of a particle in simple harmonic motion (SHM) is given by $y=\sqrt{3\pi }\sin \left(\frac{100}{\pi }t+\frac{\pi }{4}\right).$ What will be the displacement of the particle from the mean position when its kinetic energy is eight times that of its potential energy?