Mass on a Spring

Different weights are hung from various springs of different spring constants to demonstrate simple harmonic oscillations.

Materials:

  • Weights of varying masses
  • Springs with varying spring constants (white box)
  • Rod and stand with clamps to hang springs

Demo:

Hang the springs from the rod and stand and attach masses of your choice, testing them to make sure that they don’t hyper extend the springs (500g works well for the colored springs). Pull the masses down and let go to begin oscillations.

Explanation:

 

Hooke’s Law describes the force applied by a stretched spring, and depends on the spring constant, k, and the distance by which the spring is extended past its equilibrium point, x. This force is equal to the gravitational force provided by the mass, so one could calculate the stretch distance based on a given spring constant and mass.

F = ma = -kx

As you extend a spring with a mass on it, Hooke’s law applies an opposing force on the mass.

The spring constant also affects the period of the oscillating spring. When a spring stretches a distance, a restoring force is needed to move a mass, m, back to equilibrium. From the equation above, one can see that a higher mass or lower spring constant will result in a lower acceleration, causing the period of one oscillation to extend. A higher spring constant or lower mass will increase the acceleration, shortening the period. The relationship between mass, spring constant, and period can be given by the equation:

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

Where T is the period for one oscillation, m is the mass attached to the spring, and k is the spring constant.