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16 December, 10:11

The maximum potential energy of a spring system (mass 15 kg, spring constant 850 N/m) is 6.5 J. a) What is the amplitude of the oscillation? b) What is the maximum speed? c) Setting φ = 0, write the equation for the potential energy as a function of time.

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  1. 16 December, 10:31
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    a) 0.124 m

    b) 0.93 ms⁻¹

    c) 0.5 k A² cos ² (ωt)

    Explanation:

    1) Potential energy = U = 0.5 k A², where A is the amplitude and k = 850 N/m is the spring constant.

    0.5 (850) (A²) = 6.5

    ⇒ A = 0.124 m = Amplitude.

    b) From energy conservation, 0.5 m v² = 6.5

    ⇒ speed = v = 0.93 ms⁻¹

    c) If x = A cos ωt,

    Potential energy = 0.5 k A² = 0.5 k A² cos ² (ωt)
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