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20 August, 02:30

A simple harmonic oscillator completes 1550 cycles in 30 min. (a) Calculate the period. s (b) Calculate the frequency of the motion. Hz

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  1. 20 August, 02:40
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    (a) 1.16 s

    (b) 0.861 Hz

    Explanation:

    (a) Period : The period of a simple harmonic motion is the time in seconds, required for a object undergoing oscillation to complete one cycle.

    From the question,

    If 1550 cycles is completed in (30*60) seconds,

    1 cycle is completed in x seconds

    x = 30*60/1550

    x = 1.16 s

    Hence the period is 1.16 seconds.

    (b) Frequency : This can be defined as the number of cycles that is completed in one seconds, by an oscillating body. The S. I unit of frequency is Hertz (Hz).

    Mathematically, Frequency is given as

    F = 1/T ... Equation 1

    Where F = frequency, T = period.

    Given: T = 1.16 s.

    Substitute into equation 1

    F = 1/1.16

    F = 0.862 Hz

    Hence thee frequency = 0.862 Hz
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