How Do Ultrasonic Transducers Calculate Maximum Amplitude and Speed in SHM?

[wayveon]

Homework Statement

An ultrasonic transducer, of the type used in medical ultrasound imaging, is a very thin disk (m = 0.14 g) driven back and forth in SHM at 0.8 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? (in micrometers)

(b) What is the disk's maximum speed at this amplitude? (in m/s)

Homework Equations

Kinetic Energy - (1/2)(m)(v^2)
Vmax = (2pi)(f)(A)

The Attempt at a Solution

I wasn't sure whether I should be interpreting this as as spring or not, since we haven't gotten to magnets yet. So i just though, simple harmonic system have constant total energy curves, and interpreted the maximum kinetic energy of the system as being equivalent of the restoring force.

KE = (1/2)(m)(Vmax^2)

34000N = (1/2)(0.00014kg)[[2pi(0.8E6 Hz)(A)]^2]

A = sqrt( [(34000*2)/0.00014kg] / [[2pi(0.8E6 Hz)]^2] ) = 4.384e-3m, which isn't right for a. Oddly, I can see that if i don't do the square root and instead just divide the resulting quantity by two, I get the correct answer. Makes me suspect that the original solution was programmed wrong, simply slip of a ^ to a *, but I doubt myself.
Where am I going wrong with interpreting this problem? I've looked at other solutions, e.g. this one, but I haven't seen some of the other equations before frankly.

 

[rude man]

So i just though, simple harmonic system have constant total energy curves, and interpreted the maximum kinetic energy of the system as being equivalent of the restoring force.

This makes no sense to me, equating k.e. to restoring force. Instead:

SHM is x = Acos(wt), right?
So compute d²x/dt² which reveals max. acceleration. Then, F_max = m*a_max which will give you A.