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12 marksHarmonic Motion

CAPE Physics Unit 1 · 2001 · Paper 2 · Question 7(c)(i)

The human leg is modeled as a compound pendulum pivoted at the hip, with effortless walking occurring at its natural frequency. For a leg of length, l, and mass m, the natural period of oscillation is T = 2π√(I/(mgr)), where I = ml²/3 is its rotational inertia and r is the distance of the center of mass from the pivot point.

Determine, T, for a leg which is 0.9 m long, if the centre of mass is mid-way along the leg.

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Other parts of this question

  1. 7(a)Explain what is meant by mechanical resonance.[2 marks]
  2. 7(b)Describe TWO practical cases in which the resonance that occurs is desirable and TWO cases in which it is not. Explain how damping may be achieved in the…[6 marks]
  3. 7(c)(ii)Determine the speed of walking (in km h⁻¹) which is most effortless, if the person takes steps that are 0.8 m long.[1 mark]
  4. 7(c)(iii)Calculate the maximum acceleration of the leg during the walk.[1 mark]

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