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
Messages
32
Reaction score
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!
 
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.
 
Thread 'Variable mass system : water sprayed into a moving container'

Thread 'Variable mass system : water sprayed into a moving container'

Starting with the mass considerations #m(t)# is mass of water #M_{c}# mass of container and #M(t)# mass of total system $$M(t) = M_{C} + m(t)$$ $$\Rightarrow \frac{dM(t)}{dt} = \frac{dm(t)}{dt}$$ $$P_i = Mv + u \, dm$$ $$P_f = (M + dm)(v + dv)$$ $$\Delta P = M \, dv + (v - u) \, dm$$ $$F = \frac{dP}{dt} = M \frac{dv}{dt} + (v - u) \frac{dm}{dt}$$ $$F = u \frac{dm}{dt} = \rho A u^2$$ from conservation of momentum , the cannon recoils with the same force which it applies. $$\quad \frac{dm}{dt}...
View full post »

Similar threads

When Do Sand Particles Slip Off a Vibrating Plate?
Replies
13
Views
1K
Position and acceleration in simple harmonic motion given velocity
Replies
16
Views
1K
Rotating simple harmonic oscillator
Replies
11
Views
1K
Finding Parameters for Simple Harmonic Motion at t=1
Replies
1
Views
2K
Energy of particle in simple harmonic motion
Replies
13
Views
1K
Zero Amplitude Damped Simple Harmonic Motion with k=0.7s^-1 and f=3Hz
Replies
5
Views
1K
Superposition of two one-dimensional harmonic waves
Replies
10
Views
2K
What Is the Spring Constant in This Simple Harmonic Motion Problem?
Replies
2
Views
7K
Maximum compression of a spring?
Replies
2
Views
2K
Simple Harmonic Motion Question
Replies
1
Views
1K

Hot Threads

Recent Insights

Back
Top