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# Simple Harmonic motion: The Spring Pendulum. (page 2)

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Author: Jerry Silver

### Why It Works

The equation for the period of a spring pendulum (in seconds) is given by:

where m is the mass (in kilograms) and k is the spring constant (in N/m). Notice the period varies as the square root of the mass and the inverse square root of the spring constant.

### Other Things to Try

Predict and measure the period of the spring pendulum. You can do this by first finding the spring constant using the method of Project 30. You find the spring constant, k, by measuring the displacement, x, of a spring (in m) resulting from a given force, F (in N), according to the equation:

k = –F/x

The negative sign reflects the fact that force and displacement are always in the opposite direction resulting in a positive value for k.

Once you have determined the spring constant, predict the period of the spring pendulum using:

(The period will be given in seconds if the force is entered in newtons and the displacement in meters to get k. The mass must be in kg. Remember 1000g = 1kg.) Once you've called your shots, set your pendulum in motion and compare your prediction with your measured result.

### The Point

The period of a spring pendulum increases as the square root of the mass. The period of a spring pendulum increases inversely with the square root of the spring constant.

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