A horizontal spring block system of mass $M$ execute SHM  When the block is passing through its equilibrium position , an object of mass $m$ is put on it.and the two move together. Find the new amplitude and frequency of the vibration.

The amplitude of a simple pendulum, oscillating in air with a small spherical bob, decreases from 10 cm to 8 cm in 40 seconds. Assuming that Stokes law is valid, and ratio of the coefficient of viscosity of air to that of carbon dioxide is 1.3, the time in which amplitude of this pendulum will reduce from 10 cm to 5 cm in carbondioxide will be close to (ln 5 = 1.601, ln 2 = 0.693).

A pendulum with the time period of $1 \mathrm{s}$ is losing energy due to damping. At a certain time, its energy is $45 \mathrm{J}$. If after completing $15$ oscillations its energy has become $15 \mathrm{J}$, then its damping constant (in ${\mathrm{s}}^{-1}$) will be

Two pendulums $C$ and $D$ are suspended from a wire as shown in the given figure. Pendulum $C$ is made to oscillate by displacing it from its mean position. It is seen that $D$ also starts oscillating. Name the type of oscillation, $D$ will execute.

Describe an illustration of free, forced and resonant oscillations.

What is forced oscillation? Derive an expression for the amplitude of a forced oscillator when the driving frequency is far from its natural frequency.

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