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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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Answer:

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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