A pendulum bob executes small-angle oscillations in a physics laboratory
PHYSICS · Multi-part · A Level · Physics · Further mechanics and thermal physics · Further mechanics and thermal physics
Problem
A pendulum bob executes small-angle oscillations in a physics laboratory. A motion detector is placed to measure the bob’s horizontal displacement x (in meters) from its central equilibrium position. The detector display produces a position–time graph that can be described numerically as follows:
Time (s): 0.00 0.15 0.30 0.45 0.60 0.75 0.90
Position (m): +0.080 0.000 −0.080 0.000 +0.080 0.000 −0.080
Assume the data continue in the same pattern for several more cycles.
(a) Determine the amplitude of the oscillation and identify the physical meaning of the sign of x in this context.
(b) Using the numerical data, calculate the period and the frequency of the bob’s motion. Show all reasoning and include correct units.
(c) Write an explicit equation for x(t) that reproduces the data, choosing either a sine or cosine functional form. Clearly indicate any phase angle, and state the domain of time over which your expression is valid.