Simple Harmonic Motion - Mechanics - Physics Previous Year Questions

A particle is executing simple harmonic motion. If the force acting on the particle at a position is $86.6 \%$ of the maximum force on it, then the ratio of its velocity at that point and its maximum velocity is

The amplitude of a particle executing simple harmonic motion is 6 cm . The distance of the point from the mean position at which the ratio of the potential and kinetic energies of the particle becomes $4: 5$ is

At a given place, to increase the number of oscillations made by a simple pendulum in one minute from 72 to 90 , the length of the pendulum is to be decreased by

If the amplitude of a damped harmonic oscillator becomes half of its initial amplitude in a time of 10 s , then the time taken for the mechanical energy of the oscillator to become half of its initial mechanical energy is

The force ( $F$ in newton) acting on a particle of mass 90 g executing simple harmonic motion is given by $F+0.04 \pi^2 y=0$, where $y$ is displacement of the particle in metre. If the amplitude of the particle is $\frac{6}{\pi} \mathrm{~m}$, then the maximum velocity of the particle is

If the amplitudes of a damped harmonic oscillator at times $t=0, t_1$ and $t_2$ are $A_0, A_1$ and $A_2$ respectively, then the amplitude of the oscillator at a time of $\left(t_1+t_2\right)$ is