Question 1

Multiple choiceHard1 mark

An oscillator has a period of 2.0 s2.0\ \text{s} Four proposed graphs show its acceleration aa against displacement xx measured from equilibrium. Which trace is consistent with the oscillator undergoing simple harmonic motion?

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Answer: A. For simple harmonic motion, the graph of aa against xx is a straight line through the origin with gradient −ω2-\omega^2 From T=2.0 sT=2.0\ \text{s} ω=2π/T=π rad s−1\omega=2\pi/T=\pi\ \text{rad s}^{-1} so the required gradient is −π2≈−9.87 s−2-\pi^2\approx-9.87\ \text{s}^{-2} Trace P has this negative gradient and passes through the origin.
B: uses a negative gradient through the origin, but its magnitude is about 3.14 s−23.14\ \text{s}^{-2} confusing ω\omega with ω2\omega^2
C: has the required gradient but does not pass through the origin, so acceleration is not proportional to displacement.
D: has a positive gradient, so acceleration is in the direction of displacement rather than towards equilibrium.
Remember: SHM requires acceleration to be proportional to displacement and opposite in direction.

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