Simple Harmonic Motion and Maximum Speed

AI Thread Summary
The discussion revolves around calculating the maximum oscillation amplitude and speed of an ultrasonic transducer undergoing simple harmonic motion (SHM). The maximum restoring force without damaging the disk is 34,000 N, leading to an amplitude of approximately 4.784 micrometers. The user encountered difficulties calculating the maximum speed, initially arriving at 0.0450 m/s, which was deemed incorrect. The conversation includes attempts to clarify the equations used and troubleshoot the speed calculation. Ultimately, the focus remains on resolving the discrepancy in the speed calculation while confirming the amplitude result.
abeltyukov
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Homework Statement



An ultrasonic transducer, of the type used in medical ultrasound imaging, is a very thin disk (m = 0.08 g) driven back and forth in SHM at 1.5 MHz by an electromagnetic coil.(a) The maximum restoring force that can be applied to the disk without breaking it is 34,000 N. What is the maximum oscillation amplitude that won't rupture the disk?

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

Homework Equations



F = -kx
w = (2pi)f
w = (k/m)^.5
V = wA

The Attempt at a Solution



w = (2pi)(1.5E3)
w = (k/(0.08E-3)^.5 solve for k
F = -kx solve for x

I found the amplitude (part a) to be 4.784 micrometersNow I am running into problems for part b. I am trying to use V = wA and I get V = 0.0450 m/s, but that answer is not right. Any ideas on what I am doing wrong?
Thanks!
 
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M is million
 
robb_ said:
M is million

Thanks! I wonder how I got the first part right. :smile:
 
lol. I was wondering that too.
 
robb_ said:
lol. I was wondering that too.

Yeah, lol. Thanks again for your help.
 

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