Oscillations

In an oscillating spring mass system, a spring is connected to a box filled with sand. As the box oscillates, sand leaks slowly out of the box vertically so that the average frequency $\omega(t)$ and average amplitude…

Two identical tennis balls each having mass $m$and charge $q$are suspended from a fixed point by threads of length $l.$ What is the equilibrium separation when each thread makes a small angle $\theta\,$ with the…

The displacement time graph of a particle executing SHM is given in figure: (sketch is schematic and not to scale) Which of the following statements is/are true for this motion? (A) The force is zero at $t=\frac{3T}{4}$…

The point $A$moves with a uniform speed along the circumference of a circle of radius $0.36m$ and covers $30^{\circ}$ in $0.1s$. The perpendicular projection $P$ from $A$ on the diameter $MN$ represents the simple…

$Y=A\sin\,\left(\omega\,t+\varphi\,_{0}\right)$ is the time-displacement equation of a $SHM.$ At $t=0$the displacement of the particle is $Y=\frac{A}{2}$ and it is moving along negative $x$-direction. Then the initial…

For a simple harmonic motion in a mass spring system shown, the surface is frictionless. When the mass of the block is $1\mathrm{kg}$, the angular frequency is $\omega\,_{1}$. When the mass block is $2\mathrm{kg}$ the…

For particle $P$revolving round the centre $O$ with radius of circular path $r$ and regular velocity $\omega\,$, as shown in below figure, the projection of $OP$ on the $x$-axis at time $t$ is

Assume that a tunnel is dug along a chord of the earth, at a perpendicular distance $\frac{R}{2}$ from the earth's centre, where $R$ is the radius of the earth. The wall of the tunnel is frictionless. If a particle is…

A ring is hung on a nail. It can oscillate, without slipping or sliding (i) in its plane with a time period $T_{1}$ and (ii) back and forth in a direction perpendicular to its plane, with a period$T_{2}$. The…

Two particles are performing simple harmonic motion in a straight line about the same equilibrium point. The amplitude and time period for both particles are same and equal to $A$ and $T$, respectively. At time $t=0$…

A simple harmonic motion is represented by: $y=5\left(\sin\,3\pi\,t+\sqrt{3}\cos\,3\pi\,t\right)\mathrm{cm}$ The amplitude and time period of the motion are:

The time period of oscillation of a simple pendulum of length $L$suspended from the roof of a vehicle, which moves without friction down an inclined plane of inclination $\alpha\,$, is given by :