Simple Harmonic Motion and Maximum Speed

In summary, the conversation discusses the use of an ultrasonic transducer in medical ultrasound imaging. The maximum restoring force that can be applied to the disk without breaking it is 34,000 N, and the maximum oscillation amplitude is found to be 4.784 micrometers. However, there is difficulty in finding the maximum speed at this amplitude using the equation V = wA.
  • #1
32
0

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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  • #2
M is million
 
  • #3
robb_ said:
M is million

Thanks! I wonder how I got the first part right. :smile:
 
  • #4
lol. I was wondering that too.
 
  • #5
robb_ said:
lol. I was wondering that too.

Yeah, lol. Thanks again for your help.
 

What is Simple Harmonic Motion?

Simple Harmonic Motion is a type of motion exhibited by a mass attached to a spring, where the restoring force is directly proportional to the displacement from equilibrium and acts in the opposite direction.

What is the equation for Simple Harmonic Motion?

The equation for Simple Harmonic Motion is x = A sin(ωt + φ), where A is the amplitude, ω is the angular frequency, t is the time, and φ is the phase angle.

What is the maximum speed in Simple Harmonic Motion?

The maximum speed in Simple Harmonic Motion occurs at the equilibrium position and is equal to the product of the angular frequency and the amplitude, v_max = ωA.

How does mass affect Simple Harmonic Motion?

The mass does not affect the frequency or period of Simple Harmonic Motion, but it does affect the amplitude and maximum speed. A larger mass will have a smaller amplitude and maximum speed, while a smaller mass will have a larger amplitude and maximum speed.

What are some real-life examples of Simple Harmonic Motion?

Some real-life examples of Simple Harmonic Motion include the motion of a pendulum, the motion of a mass on a spring, and the motion of a mass attached to a rope being pulled by an oscillating object.

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