Question

An object swings from the end of a cord as a simple pendulum with period T. An identical object oscillates up and down on the end of a vertical spring with the same period T. If the masses of both objects are doubled, how will the new values of the periods compare to T?

Answer 1

The period of a pendulum can be calculated by knowing the acceleration of gravity and the length of the pendulum.

`T = 2pi sqrt(L/g)`

The mass of the pendulum doesn't figure into the equation. While it is true that twice as much force will be required to accelerate a mass that is twice as large, the gravitational force increases as we increase the mass.

The period of a simple spring depends on the spring constant `k` and the mass `m`.

`T = 2pi sqrt(m/k)`

Where m is the mass of the object and k is the spring constant. If we replace m with 2m, we can calculate that the period will increase by `sqrt(2)`.

`T' = sqrt(2)T` for the spring-mass system.