A student investigates the small-angle oscillations of a thin uniform wooden rod of length LLL pivoted at one of its ends.
Describe how to determine accurately the period TTT of oscillations of this rod.
The relationship between the frequency fff of the oscillations of the rod and its length LLL is given by:
f=12π3g2L f = \frac{1}{2\pi}\sqrt{\frac{3g}{2L}} f=2π12L3gwhere ggg is the acceleration of free fall.
The student varies the length LLL of the rod and determines the period TTT for each length. The student plots a graph of T2T^2T2 against LLL.
Show that the gradient of the graph is given by the equation:
gradient=8π23g \text{gradient} = \frac{8\pi^2}{3g} gradient=3g8π2The gradient of the line of best fit on the student's graph is 2.74 s2 m−12.74\text{ s}^2\text{ m}^{-1}2.74 s2 m−1. Use this value to determine ggg.
The student draws a line of worst fit and determines its gradient to be 2.85 s2 m−12.85\text{ s}^2\text{ m}^{-1}2.85 s2 m−1. Use this line of worst fit to calculate the percentage uncertainty in ggg.
Use the accepted value of g=9.81 m s−2g = 9.81\text{ m s}^{-2}g=9.81 m s−2 to evaluate the accuracy of the student's experimental value of ggg. Include a calculation of the percentage difference in your answer.
39 exam-style questions on OCR A A Level Physics Oscillations, covering Simple harmonic oscillations, Energy of a simple harmonic oscillator, and Damping. Each one has a worked solution and a mark scheme showing where the marks go.