In an angular S.H.M. angular amplitude of oscillation is $\pi$ $\mathrm{rad}$ and the time period is$0.4$ $\mathrm{s}$ then calculate its angular velocity at angular displacement $\frac{\pi }{2}$ $\mathrm{rad}$.

A spring is oscillating with frequency $4 \mathrm{Hz}$ having spring constant $k$. An identical spring is connected in series in new system as shown in figure. Find the new frequency.

A spring of force constant $k$ is cut into lengths of ratio $1:2:3$. They are connected in series and the new force constant is $k^{\text{'}}$. Then, they are connected in parallel and force constant is $k^{\text{'}\text{'}}$. Then, $k^{\text{'}}:k^{\text{'}\text{'}}$ is,

Two sound waves having pressure, $P_1=2\times {10}^4\sin (2\pi \times {10}^{4}t) \mathrm{Pa}$ and $P_2=4\times {10}^4\sin \left(3\pi \times {10}^{4}t+\left(\frac{\pi }{6}\right)\right) \mathrm{Pa}$ superimpose each other. Find the amplitude of resultant wave.