Engineering Physics

A spring is stretched by $5\,\mathrm{cm}$ when a load of $1\,\mathrm{kg}$ is suspended to the lower end (upper end of spring is fixed). What will be the maximum velocity of object if it is pulled down further by $5\,\mathrm{cm}$ from equilibrium position and then released?

Prove that average kinetic and average potential energies of a particle executing simple harmonic motion are equal.

Deduce the time period of a simple harmonic vibration. Explain why a loaded bus is more comfortable than an empty bus.