Oscillations

A body is performing simple harmonic with an amplitude of $10\mathrm{cm}$. The velocity of the body was tripled by air Jet when it is at $5\mathrm{cm}$ from its mean position. The new amplitude of vibration is…

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:

A pendulum bob has a speed of $3ms^{-1}$at its lowest position. The pendulum is $50\mathrm{cm}$ long. The speed of bob, when the length makes an angle of $60^{\circ}$ to the vertical will be…

The metallic bob of simple pendulum has the relative density $5$. The time period of this pendulum is $10s$. If the metallic bob is immersed in water, then the new time period becomes $5\sqrt{x}s$. The value of $x$ will…

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

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 :

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…

A particle performs simple harmonic motion with a period of $2$ second. The time taken by the particle to cover a displacement equal to half of its amplitude from the mean position is $\frac{1}{a}s.$ The value of $a$ to…

Two bodies of masses $1\mathrm{kg}$ and $4\mathrm{kg}$ are connected to a vertical spring, as shown in the figure. The smaller mass executes simple harmonic motion of angular frequency $25\rad\,s^{-1}$, and amplitude…

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 oscillator has an amplitude $A$ and time period $6\pi\,$ second. Assuming the oscillation starts from its mean position, the time required by it to travel from$x=A$ to $x=\frac{\sqrt{3}}{2}A$ will be…

An oscillator of mass$M$ is at rest in its equilibrium position in a potential,$V=\frac{1}{2}k\left(x-X\right)^{2}$ . A particle of mass$m$ comes from the right with speed$u$ and collides completely inelasticwith$M$ and…