What Is the Maximum Oscillation Amplitude for an Ultrasonic Transducer?

AI Thread Summary
The discussion focuses on calculating the maximum oscillation amplitude and speed of an ultrasonic transducer used in medical imaging. The maximum restoring force before rupture is 36,000 Newtons, and the mass of the disk is 0.12 grams. Participants are seeking to derive the amplitude in micrometers and the maximum speed in meters per second. The conversation highlights the need to connect the equations of motion for simple harmonic motion (SHM) to find these values. Understanding the relationships between force, mass, and acceleration is crucial for solving the problem.
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An ultrasonic transducer, of the type used in medical ultrasound imaging, is a very thin disk (m = 0.12 g) driven back and forth in SHM at 0.9 MHz by an electromagnetic coil.
(a) The maximum restoring force that can be applied to the disk without breaking it is 36,000 Newtons. What is the maximum oscillation amplitude that won't rupture the disk?
(in µm)

(b) What is the disk's maximum speed at this amplitude?
(in m/s)

For position, I would guess to use x = Acos(omega*t)
I cannot tie the proper equations together, though. Help would be appreciated. Thanks.
 
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You know mass and force. What quantity is determined by their ratio?

You wrote correctly the time dependence of position in SHM. What about velocity and acceleration?

ehild
 

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