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?

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