Simple Harmonic Motion and Maximum Speed

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SUMMARY

The discussion centers on calculating the maximum oscillation amplitude and maximum speed of an ultrasonic transducer operating in Simple Harmonic Motion (SHM) at a frequency of 1.5 MHz. The maximum restoring force without rupture is 34,000 N, leading to a calculated amplitude of 4.784 micrometers. However, the user encountered difficulties calculating the maximum speed, initially arriving at 0.0450 m/s, which was incorrect. The correct application of the formula V = wA is essential for accurate results.

PREREQUISITES
  • Understanding of Simple Harmonic Motion (SHM)
  • Familiarity with the formula F = -kx for restoring force
  • Knowledge of angular frequency calculation w = (2πf)
  • Ability to apply V = wA for maximum speed determination
NEXT STEPS
  • Review the derivation of the spring constant k from F = -kx
  • Study the relationship between frequency and angular frequency in SHM
  • Practice solving problems involving maximum speed in SHM using V = wA
  • Explore the effects of varying mass on oscillation amplitude and speed
USEFUL FOR

Students studying physics, particularly those focusing on mechanics and oscillatory motion, as well as educators seeking to clarify concepts related to Simple Harmonic Motion and its applications in ultrasonic technology.

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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