Time-period of a particle in S.H.M. depends on the force constant k and mass m of the particle. Explain

Question

Time-period of a particle in S.H.M. depends on the force constant k and mass m of the particle. T = 2π√{m/k}. A simple pendulum executes the S.H.M. approximately. Why then is the period of a pendulum independent of the mass of the pendulum? Explain.

Answer 1

In case of a spring, k does not depend upon 'm'. However in case of a simple pendulum, k is directly proportional to m and hence the ratio (m/k) is a constant quantity.