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Damped oscillator: time for the amplitude to halve or the damping constant

This type of question, asked 2 times: 2021 Paper 6, 2021 Paper 8. All 2 questions below, oldest first.

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  1. Question 1

    2021 Paper 6

    18
    Amplitude of a mass-spring system, which is executing simple harmonic motion decreases with time. If mass =500 g= 500\text{ }g, Decay constant =20 g/s= 20\text{ }g/s then how much time is required for the amplitude of the system to drop to half of its initial value? (ln⁡2=0.693)(\ln2 = 0.693)

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  2. Question 2

    2021 Paper 8

    3
    A block of mass 1 kg1\text{ }kg attached to a spring is made to oscillate with an initial amplitude of 2 cm2\text{ }cm. After 2 minutes the amplitude decreases to 1 cm1\text{ }cm. Determine the value of the damping constant for this motion. (take ln⁡2=0.693\ln 2 = 0.693)

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