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13 June, 22:26

The maximum restoring force that can be applied to the disk without breaking it is 29,000 N. What is the maximum oscillation amplitude that won't rupture the disk?

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  1. 13 June, 23:43
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    The Amplitude is 7.34 * 10^6m

    Explanation: complete question (The ultrasonic transducer used in a medical ultrasound imaging device is a very thin disk (m = 0.10 g) driven back and forth in SHM at 1.0 MHz by an electromagnetic coil.)

    From Newton's 2nd law, the force F on a body with mass, m is related to its acceleration by:

    F = ma ... eq1

    The maximum transverse speed and acceleration of a particle in simple Harmonic motion are found in terms of the angular speed and amplitude

    Vmax=wa ... eq2

    amax = w^2A ... eq3

    The angular frequency w of a wave is related to the frequency by:

    w = 2pif ... eq4

    Fmax = mw^2A

    Fmax = m (2pif) ^2A

    Fmax = 4pi^2mf^2A

    Where Fmax = maximum restoring force

    m = mass of disk

    f = frequency of disk

    A = Fmax/[4pi^2 * (0.10*10^-3) * (1.0*10^6) ^2]

    A = 29000 / [4x (3.142) ^2 * (0.10*10^-3) * (1.0*10^6) ^2]

    A = 29000 / (3948865600)

    A = 7.34*10^-6m
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