Due to some force $F_1$,a body oscillates with a period of $4/5 \, s$,and due to another force $F_2$,it oscillates with a period of $3/5 \, s$. If both forces act simultaneously,the new period will be .... $s$.

The displacement-time graph of a particle executing $SHM$ is shown. Which of the following statements is wrong?

Consider two identical cylinders (each of mass $m$,density $\rho_0$,horizontal cross-section area $s$) in equilibrium,partially submerged in two containers filled with liquids of densities $\rho_1$ and $\rho_2$ as shown in the figure. Find the period of small oscillations of this system about its equilibrium. Neglect the changes in the level of liquids in the containers. Neglect the mass of the strings. The acceleration due to gravity is $g$. ($v$ is the volume of each block).

$A$ graph of the square of the velocity against the square of the acceleration of a given simple harmonic motion is

An ideal gas enclosed in a vertical cylindrical container supports a freely moving piston of mass $M$. The piston and the cylinder have equal cross-sectional area $A$. When the piston is in equilibrium, the volume of the gas is $V_0$ and its pressure is $P_0$. The piston is slightly displaced from the equilibrium position and released. Assuming that the system is completely isolated from its surroundings, the piston executes a simple harmonic motion with frequency

$Assertion :$ In simple harmonic motion,the velocity is maximum when the acceleration is minimum.
$Reason :$ Displacement and velocity of $S.H.M.$ differ in phase by $\frac{\pi }{2}$.