An oscillating pendulum suspended from the roof of a lift which is at rest has time period $T_1$. When lift moves up with acceleration 'a' its time period is $T_2$. When lift moves down with acceleration 'a' its time period is $T_3$. The relation between $T_1$, $T_2$ and $T_3$ is

A mass $0.4$ kg performs S.H.M. with a frequency $\dfrac{16}{\pi}$ Hz. At a certain displacement it has kinetic energy $2$ J and potential energy $1.2$ J. The amplitude of oscillation is

A mass attached to a spring performs S.H.M. whose displacement is $x = 3 \times 10^{-3} \cos 2\pi t$ m. The time taken to obtain maximum speed for the first time is (in s)

The closed and open organ pipe have same length and when they are vibrating simultaneously in first overtone produce $3$ beats. The length of open pipe is made $\left(\dfrac{1}{3}\right)^{rd}$ and closed pipe is made $3$ times the original, the number of beats produced will be {neglect end correction}