Time period of a particle in SHM is `T=2pisqrt(m/k)`. A simple pendulum executes SHM approximately. Why then is the time period of pendulum is independent of mass?

What is the time period of a second’s pendulum?

A simple pendulum is an object suspended by a weightless and inextensible string fixed rigidly to a support. The period of oscillation of the pendulum is T. What will be the period if the pendulum is suspended in a lift moving down with an acceleration equal to g/3 .

A student is advised to study the variation of period of oscillation with the length of a simple pendulum in the laboratory. Accordingly he recorded the period of oscillation for different lengths of the pendulum. How would you determine the value of acceleration due to gravity using L-T^2 graph?