# 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?

Nov 28, 2014

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

$T = 2 \pi \sqrt{\frac{L}{g}}$

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 $m$.

$T = 2 \pi \sqrt{\frac{m}{k}}$

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.