A bob of a simple pendulum has mass $m$ and is oscillating with an amplitude $a$. If the length of the pendulum is $L$, then the maximum tension in the string is $\left[\cos 0^{\circ}=1\right.$, $g=$ acceleration due to gravity]

A body of mass 64 g is made to oscillate turn by turn on two different springs $A$ and $B$. Spring $A$ and $B$ has force constant $4 \frac{\mathrm{~N}}{\mathrm{~m}}$ and $16 \frac{\mathrm{~N}}{\mathrm{~m}}$ respectively. If $T_1$ and $T_2$ are period of oscillations of springs $A$ and $B$ respectively, then $\frac{T_1+T_2}{T_1-T_2}$ will be

The damping force of an oscillator is directly proportional to the velocity. The unit of constant of proportionality is

A particle performs simple harmonic motion with period of 3 s . The time taken by it to cover a distance equal to half the amplitude from mean position is [$$\sin 30^{\circ}=0.5$$]