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5 marksHarmonic Motion

CAPE Physics Unit 1 · 2009 · Paper 2 · Question 2(c)(ii)

The depth of water h at a harbour varies with time t according to the equation h = 9 + 5.0 sin (ωt), where h is in metres, t is in seconds, and ω is 1.45 x 10⁻⁴ rad s⁻¹.

Calculate the two values of t, (t₁ and t₂), for which the water is 11.5 m deep. (Give the answer in hours).

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Other parts of this question

  1. 2(a)(i)Explain what is meant by 'periodic motion'.[1 mark]
  2. 2(a)(ii)Explain what is meant by 'simple harmonic motion'.[2 marks]
  3. 2(b)Describe the practical procedures that you would follow to obtain such a graph for this harbour.[5 marks]
  4. 2(c)(i)For this harbour, calculate the MINIMUM depth of the water.[1 mark]
  5. 2(c)(iii)Calculate the length of time for EACH tide during which the depth of water is MORE than 11.5 metres.[1 mark]

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