Simple Harmonic Motion and Maximum Speed

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Homework Help Overview

The discussion revolves around a problem involving simple harmonic motion (SHM) related to an ultrasonic transducer used in medical imaging. The original poster is tasked with determining the maximum oscillation amplitude and maximum speed of the transducer based on given parameters.

Discussion Character

  • Exploratory, Mathematical reasoning, Problem interpretation

Approaches and Questions Raised

  • The original poster attempts to calculate the maximum amplitude using the relationship between force and spring constant, while also exploring the maximum speed using the amplitude and angular frequency. Some participants express curiosity about the correctness of the original poster's calculations.

Discussion Status

The discussion is ongoing, with the original poster having successfully calculated the amplitude but encountering difficulties with the maximum speed calculation. Participants are engaging with the original poster's findings and expressing interest in the problem.

Contextual Notes

The original poster's calculations involve specific values and relationships from physics, including the maximum restoring force and the frequency of oscillation. There is an indication of uncertainty regarding the correctness of the speed calculation.

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!
 
Physics news on Phys.org
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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