3.6.1.3
Required practical: investigating SHM with a simple pendulum
Simple Harmonic Motion — AQA A-Level Physics
- Aim: determine g by investigating how T varies with pendulum length L.
- Independent variable: length L. Dependent variable: time periodThe time taken for one complete oscillation or wave cycle. Measured in seconds (s). T.
- Control variables: mass of bob, number of oscillations, amplitudeThe maximum displacement of a point on a wave from its equilibrium (rest) position. Measured in metres (m). (small angle).
Method
- Set string length to 0.2 m. Pull bob to small angle (< 10 degrees) and release.
- Time 10 complete oscillations and divide by 10 for mean T.
- Increase length in steps up to 2.0 m and repeat.
- Measure L from the pivot to the centre of mass of the bob.
Analysis: plot \(T^{2}\) against L
- From T = 2 pi sqrt(L/g), squaring gives \(T^{2}\) = (4 pi^2 / g) L.
- Plot \(T^{2}\) (y-axis) against L (x-axis).
- $Gradient = 4 \pi^2 / g. So g = 4 \pi^2 / gradient.$
- Compare obtained g to accepted value (9.81 m \(s^{-2}\)) to assess accuracyHow close a measurement is to the true or accepted value. High accuracy means low systematic error..
$$g = \frac{4\pi^2}{\text{gradient}}$$
- $g$: gravitational field strengthThe gravitational force per unit mass at a point in a gravitational fieldA region of space in which a mass experiences a gravitational force.. Measured in N kg⁻¹. (m \(s^{-2}\))
- $gradient$: gradient of \(T^{2}\) vs L graph (\(s^{2}\) \(m^{-1}\))