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}

Two uniform wires of same material are vibrating under the same tension. If the first overtone of the first wire is equal to the second overtone of the second wire and radius of first wire is twice the radius of second wire then the ratio of length of first to second wire is