Embibe Experts Solutions for Exercise 3: EXERCISE 13.3

Time period of the block in the shown system is

Two particles $A$ and $B$ of equal masses are suspended from two massless springs of spring constants $k_1$ and $k_2$, respectively. If the maximum velocities, during oscillations are equal, the ratio of amplitudes of $A$ and $B$ is

One end of a spring of force constant $k$ is fixed to a vertical wall and the other end is connected to a block of mass $m$ resting on a smooth horizontal surface as shown. The spring is now compressed by $2a$ and released. The time after which the block will strike the other wall is

A block $P$ having mass $m$ is placed on a horizontal frictionless plane. Another block having same mass is placed on it and is connected to a spring of spring constant $k.$ The two blocks are pulled by a distance $A$ and released. Block $Q$ oscillates without slipping. The maximum value of frictional force between two blocks is

Two blocks $A$ and $B$ of masses $0.3 \mathrm{kg}$ and $0.4 \mathrm{kg}$ respectively are stuck to each other by some weak glue as shown is the figure. They hang together at end of a spring with a spring constant $k=200 \mathrm{N} {\mathrm{m}}^{-1}$. The block $B$ suddenly falls free due to failure of glue.

Find
(i) Period of SHM of block $A$
(ii) Amplitude of its SHM of block $A$
(iii) Total energy of oscillation

A mass $M$ is suspended from a spring of negligible mass. The spring is pulled a little and then released, so that, the mass executes SHM of the time period $T$. If the mass is increased by $m$, the time period becomes $\frac{5T}{3}$. Then the ratio of $\frac{m}{M}$ is,