Simple Harmonic Motion (mass spring system)

Question 1

Equipment

Answer 1

○ Spring

○ 50g masses with 50g holder

○ Stand and clamp

○ Pin and blu-tack

○ Metre ruler

○ Stopwatch

Question 2

Method

Answer 2

○ Set up the apparatus as shown in the diagram, with no masses slotted on the 50g holder.

○ Pull the mass hanger vertically downwards a few centimetres and release it. Start the stopwatch when it passes the fiducial marker (pin and blu-tack at the centre).

○ Stop the stopwatch after 10 complete oscillations and record this time . Divide T10 T by 10 to find the time period T of the mass-spring system and record this. 10

○ Add a 50g mass to the 50g holder and repeat this, adding 50g each time up to 500g, recording the total hanging mass m and corresponding time period T for each.

○ Repeat the experiment twice more and find and record the mean T for each m.

Question 3

Graphs and calculations:

Answer 3

○ Plot a graph of T^2 against m and draw a line of best fit. The gradient will be 4π^2 divided by the spring constant.

T = 2π √m/k ⇒ T^2 = 4π^2/k x m

Question 4

Safety

Answer 4

○ Suspended masses could be dangerous if the masses fall off and injure someone. To avoid this, only pull down the spring by a few centimetres and don’t attach too heavy masses to the spring.

Question 5

Improvements and notes

Answer 5

○ If the spring starts to move horizontally during its oscillation, stop the oscillation and start it again making sure it is pulled vertically downwards.

○ Timing more oscillations for each mass reduces the percentage uncertainty in the time period.

○ The fiducial marker should be at the centre of the oscillation (equilibrium position) so the mass is moving past it at the fastest speed and there is the least uncertainty in starting and stopping the stopwatch.

○ A motion tracker and data logger can be used to find a more accurate value for the time period and eliminating random error in starting and stopping the stopwatch.

Question 6

Diagram

Answer 6