Preparation and setup

1. Hang the spring from a clamp and attach the 100 g mass hanger.

2. Position the Blu-Tack and pin at the bottom of the mass as a reference point. This will represent the centre of the subsequent oscillations.

Conducting the experiment

1. Pull the mass hanger vertically downwards a few centimetres and release. The spring should oscillate vertically up and down.

2. Determine the time period of the mass-spring system by timing 10 complete oscillations.

3. Take repeat readings of the time for 10 oscillations, T10. Use the values of T10 to find the time period for one oscillation, T.

4. Add a 100 g mass to the mass hanger and repeat the timing process to enable the time period of the oscillations to be found.

Repeat the experiment

1. Repeat the experiment with a range of different masses, m, and for each mass determine the corresponding time period, T.

Calculations and Analysis

1. Plot a graph of T2 on the y-axis against m.

2. A straight line through the origin will confirm the relationship between T and m predicted by SHM theory ie T²= 4π²m / k where k is the spring constant or stiffness of the spring.

3. The gradient of the graph can be used to determine k.

   T² = 4πm / k hence k= 4π² / gradient

4. Estimate the uncertainty in T and m. Hence find the uncertainty in k.