Graphs of simple harmonic motionEdexcel International A Level Physics: Mind map

Exam questions on Graphs of simple harmonic motion

1. A mass hangs from a spring and oscillates vertically with simple harmonic motion, with an amplitude of 5.0 cm and a period of 2.0 s. A data logger plots the displacement of the mass against time, taking upwards as positive. At t = 0 the mass is at its maximum upward displacement, so the displacement–time graph is a cosine curve.
   Use the gradient of the displacement–time graph to describe how the velocity of the mass changes between t = 1.0 s and t = 2.0 s.2 marks
2. For the same oscillating mass (amplitude 5.0 cm, period 2.0 s, released from maximum upward displacement at t = 0), the data logger also plots velocity against time, with upwards as positive. The velocity is given by v = −0.157 sin(πt), where v is in m s⁻¹ and t is in s, so the velocity–time graph is a negative sine curve.
   Calculate the gradient of the velocity–time graph at t = 0 and state what this gradient represents.2 marks
3. A trolley oscillates horizontally between two springs with simple harmonic motion. Its amplitude is 8.0 cm and its period is 1.6 s. It is at its maximum positive displacement at t = 0, so the graph of displacement against time is a cosine curve.
   Describe how the gradient of the displacement–time graph changes during one complete oscillation, and say what this shows about the velocity of the trolley at t = 0, 0.40 s and 0.80 s.3 marks