For two masses attached to a spring as shown in the diagram, prove that the effective inertial mass of the system is given by

$\mu =\frac{m_1{m}_2}{m_1+m_2}$

The point $A$ moves with a uniform speed along the circumference of a circle of radius $0.36 \mathrm{m}$ and covers $30°$ in $0.1 \mathrm{s}$. The perpendicular projection $P$ from $A$ on the diameter $MN$ represents the simple harmonic motion of $P$. The restoration force per unit mass when $P$ touches $M$ will be :

A load of mass $m$ falls from a height $h$ on the scale pan hung from a spring as shown. If the spring constant is $k$ and the mass of the scale pan is zero and the mass $m$ does not bounce relative to the pan, then the amplitude of vibration is 

A solid block on a frictionless surface is connected to two rigid supports on the left and right side by springs of spring constants $k$ and $4k$ respectively as shown in the figure. The time spent by the block in a complete cycle of oscillation on the left and the right side of the equilibrium position are $t_L$ and $t_R$ respectively. Which of the following is correct?

A system is shown in the figure. The time period for small oscillations of the two blocks will be

The time period for small vertical oscillations of a block of mass $\mathrm{m}$ when the masses of the pulleys are negligible and spring constant ${\mathrm{k}}_1$ and ${\mathrm{k}}_2$ is

A $10 \mathrm{kg}$ body is suspended from an ideal spring (force constant $250 {\mathrm{Nm}}^{-1}$.) How much time it will take in reaching its mean position from its position of maximum displacement?

Two blocks connected by a spring rest on a smooth horizontal plane as

Shown in diagram. A constant force F starts acting on the block m₂

Two blocks connected by a spring rest on a smooth horizontal plane as


Shown in diagram. A constant force F starts acting on the block m₂

Compute the time period for the following system if the block of mass $m$ is slightly displaced vertically down from its equilibrium position and then released. Assume that the pulley is light and smooth, strings and springs are light.