Two particle performs simple harmonic motion with time period of $6$ second and$7$second respectively. At $t=0$ both were in their mean position and moving in the same direction. After what minimum non zero time they will be in phase again.

A simple pendulum suspended from the ceiling of a stationary lift has a time period $T_0$. When the lift descends at uniform speed, the time period is $T_1$. When the lift descends with constant acceleration, the time period is $T_2$. Which of the following is correct?

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 

An ideal gas enclosed in a vertical cylindrical container supports a freely moving piston of mass $\mathit{\text{M}}$. The piston and the cylinder have equal cross-sectional area $\mathit{\text{A}}$. When the piston is in equilibrium, the volume of the gas is $V_0$ and its pressure is $M_0$. The piston is slightly displaced from the equilibrium position and released. Assuming that the system is completely isolated from its surrounding, the piston executes a simple harmonic motion with frequency
[Assume the system is in space.]

Match List$‐\mathrm{I}$ (Event) with List$‐\mathrm{II}$ (Order of the time interval for the happening of the event) and select the correct option from the options given below the lists.