Answer the following questions:
(a) Time period of a particle in SHM depends on the force constant and mass of the particle: . A simple pendulum executes SHM approximately. Why then is the time period of a pendulum independent of the mass of the pendulum?
(b) The motion of a simple pendulum is approximately simple harmonic for small-angle oscillations. For larger angles of oscillation, a more involved analysis shows that is greater than Think of a qualitative argument to appreciate this result.

(a) The spring constant is proportional to the mass in the case of a simple pendulum. The numerator () and denominator () will cancel each other out. As a result, the simple pendulum’s time period is independent of the bob’s mass.

(b) The expression for the restoring force acting on the bob of a basic pendulum is

restoring force

mass of the bob

acceleration due to gravity

angle of displacement

When is small, .

Then the expression for the time period of a simple pendulum is given by

when is huge. As a result, the equation above is invalid. In the time period , there will be an increase.