Embibe Experts Solutions for Chapter: Oscillations, Exercise 1: BITSAT 2017

The time period of a bob performing simple harmonic motion in water is $2 \mathrm{s}$. If density of bob is $\frac{4}{3}\times {10}^3 \mathrm{kg} {\mathrm{m}}^{-3}$, then time period of bob performing simple harmonic motion in air will be

Frequency of oscillation of a body is $5 \mathrm{Hz}$ when a force $F_1$ is applied and $12 \mathrm{Hz}$ when another force $F_2$ is applied. If both forces $F_1$ and $F_2$ are applied together, then frequency of oscillation of the body will be

The bob of simple pendulum is a spherical hollow ball filled with water. A plugged hole near the bottom of the oscillating bob get suddenly unplugged. During observation, till water is coming out, the time period of oscillation would

If $x, v$ and $a$ denote the displacement, the velocity and the acceleration of a particle executing $SHM$ of time period $T$. Then, which of the following does not change with time?

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

A rectangular block of mass $m$ and area of cross-section $A$ floats in a liquid of density $\rho$. If it is given a vertical displacement from equilibrium, it undergoes oscillation with a time period $T$. Then

A load of mass $m$ falls from a height $h$ on the scale pan hung from a spring as shown. If the spring constant is $k$ and the mass of the scale pan is zero and the mass $m$ does not bounce relative to the pan, then the amplitude of vibration is 

Two simple pendulums of lengths $5 \mathrm{m}$ and $20 \mathrm{m}$ respectively are given small displacement in one direction at the same time they will again be in the same sense when the pendulum of shorter length has completed $n$ oscillations. Then, $n$ is