Ultrasonic transducer pretty much another SHM problem

[<3Science]

Homework Statement

An ultrasonic transducer, of the type used medical ultrasound imaging, is avery thin disk (m=0.10 g) driven back and forth in SHM at 1.0 MHz by an electromagnetic coil.

a. The maximum restoring force that can be applied to the disk without breaking it is 40,000 N. What is the maximum oscillation amplitude that won't rupture the disk?

Homework Equations

f = 1/2pi * sqrt (k/m)
Fsp = -kx

The Attempt at a Solution

I figured I could get k so I went

k = m(2(pi)f) ^2
k = (0.00010 kg) (2pi * 1.0*10^6 Hz) = 628

And then put it into the second equation to get max amplitude

40,000 N = 628 x

x = 63.66 ... m ? It's however not correct the answer is supposed to be 10.1 micrometers

 

[tiny-tim]

welcome to pf!

hi <3Science! welcome to pf!

(have a pi: π and try using the X² icon just above the Reply box )

k = m(2(pi)f) ^2
k = (0.00010 kg) (2pi * 1.0*10^6 Hz) = 628

erm … squared?