3.6.1.3
Required practical: investigating SHM with a mass-spring system
Simple Harmonic Motion — AQA A-Level Physics
- Aim: determine the spring constantThe force per unit extension of a spring. A measure of the stiffness of the spring. Measured in N m⁻¹. k by investigating how T varies with mass m.
- Independent variable: mass m. Dependent variable: time periodThe time taken for one complete oscillation or wave cycle. Measured in seconds (s). T.
- Control variables: spring constantThe force per unit extension of a spring. A measure of the stiffness of the spring. Measured in N m⁻¹. k, number of oscillations, amplitudeThe maximum displacement of a point on a wave from its equilibrium (rest) position. Measured in metres (m)..
Method
- Attach mass to spring and pull down 2-5 cm. Release and time 10 complete oscillations.
- Divide total time by 10 to get the mean periodThe time taken for one complete oscillation or wave cycle. Measured in seconds (s). T.
- Add 50 g masses and repeat for 8-10 different masses.
- Use a fiducial marker (needle) at the equilibriumAn object is in equilibrium when the resultant force on it is zero. The object is either stationary or moving at constant velocityThe rate of change of displacement. A vector quantity. Measured in m s⁻¹.. position to count oscillations accurately.
Analysis: plot \(T^{2}\) against m
- From T = 2 pi sqrt(m/k), squaring gives \(T^{2}\) = (4 pi^2 / k) m.
- This is $y = mx$ form. Plot \(T^{2}\) (y-axis) against m (x-axis).
- $Gradient = 4 \pi^2 / k. So k = 4 \pi^2 / gradient.$
- The line should pass through the origin.
$$k = \frac{4\pi^2}{\text{gradient}}$$
- $k$: spring constantThe force per unit extension of a spring. A measure of the stiffness of the spring. Measured in N m⁻¹. (N \(m^{-1}\))
- $gradient$: gradient of \(T^{2}\) vs m graph (\(s^{2}\) kg^{-1})