Oscillations

Four massless springs whose force constants are $2 k, 2 k, k$ and $2 k$ respectively are attached to a mass $\mathrm{M}$ kept on a frictionless plane (as shown in figure). If the mass $M$ is displaced in the horizontal…

A simple pendulum doing small oscillations at a place R height above earth surface has time period of $T_1=4 \mathrm{~s}$. $T_2$ would be it's time period if it is brought to a point which is at a height $2 R$ from…

A particle executes SHM of amplitude A. The distance from the mean position when it's kinetic energy becomes equal to its potential energy is

In a resonance column first and second resonance are obtained at depths $24 \mathrm{~cm}$ and $78 \mathrm{~cm}$ the third resonance will be obtained at depth.

In a simple pendulum of length I the bob is pulled aside from its equilibrium position through an angle $\theta$ and then released. The bob passes through the equilibrium position with speed

A particle executing simple harmonic motion along $y$ -axis has its motion described by the equation $y=A \sin (\omega t)+B$. The amplitude of the simple harmonic motion is

An instantaneous displacement of a simple harmonic oscillator is $x=A \cos (\omega t+\pi / 4)$. Its speed will be maximum at time

Frequency of oscillation of a body is $5 \text{Hz}$ when a force ${F}_{1}$ is applied and $12 \text{Hz}$ when another force ${F}_{2}$ is applied. If both forces ${F}_{1}$ and ${F}_{2}$ are applied together, then…

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

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?

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…

Two simple pendulums of lengths $5 m$ and $20 m$ 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 $n$…