Starting from the origin, a body oscillates simple harmonically with a period of $2 \mathrm{s}$. After what time will its kinetic energy be $75\%$ of the total energy?

A wooden Cube (density of wood d) of side $1$ floats in a liquid of density $\rho$ with its upper and lower surfaces horizontal. If the cube is pushed slightly down and released, it performs simple harmonic motion of period $T$, then $T$ is given by

A particle of mass $m$ is located in a one-dimensional potential field whose potential energy is given by $V\left(x\right)=\mathrm{A}[1-\cos px]$, where $A$ and $p$ are constants. The period of small oscillations of the particle

A particle executes s.h.m. of amplitude $25 \mathrm{cm}$ and time period $3 \mathrm{s}$. What is the minimum time required for the particle to move between two points $12.5 \mathrm{cm}$ on either side of the mean position?

Two identical springs are connected to a mass $m$ as shown in Fig. 22.67 ($k=$spring constant). If the period of the configuration in (a) is $2 \mathrm{s}$, the period of the configuration in (b) is

Two springs are joined and attached to a mass of $16 \mathrm{kg}$. This system is then suspended vertically from a rigid support. The spring constant of the springs are $k_1$ and $k_2$ respectively. The period of vertical oscillations of the system will be