A mass on the end of a horizontal spring is displaced from its equilibrium position by a distance $A$ and released. Its subsequent oscillations have total energy $E$ and time period $T$.

An identical mass is attached to an identical spring. The maximum displacement is ${\text{2}}A$. Assuming this spring obeys Hooke’s law, which of the following gives the correct time period and total energy?

A

The time period is unaffected by a change in amplitude but the energy is directly proportional to the square of the amplitude. A mass oscillating on a spring is not explicitly mentioned on the syllabus but like the simple pendulum, it is an integral component of Simple Harmonic Motion (SHM).