# Determine freq of AC that induces stress in the specimen

1. Oct 9, 2014

### Dustinsfl

1. The problem statement, all variables and given/known data
An electromagnetic fatigue-testing machine has an alternating force is applied to the specimen by passing an alternating current of frequency $f$ through the armature. If the weight of the armature is $40$ lb, the stiffness of the spring $k_1$ is $10217.0296$ lb/in, and the stiffness of the steel specimen is $75\times 10^4$ lb/in, determine the frequency of the alternating current that induces stress in the specimen that is twice the amount generated by the magnets.

2. Relevant equations
$m\ddot{x} + (k_1 + k_2)x = F_0\sin(\omega t)$

3. The attempt at a solution
I have found the equation of motion:
$$x(t) = A\cos(431.571t) + B\sin(431.571t) + \frac{F_0/m}{431.571^2 - \omega^2}\sin(\omega t)$$
where $m = W/g = 4.08163$ and $\omega_n = \sqrt{\frac{k_1 + k_2}{m}} = 431.571$.

The answer is $f = 743.7442$ Hz. I have no idea how I am supposed to obtain this answer. I know if I can find $\omega$, then $f = \frac{\omega}{2\pi}$, but I don't know how can I can go about finding $\omega$.

2. Oct 14, 2014

### Greg Bernhardt

Thanks for the post! Sorry you aren't generating responses at the moment. Do you have any further information, come to any new conclusions or is it possible to reword the post?

3. Oct 14, 2014

### Staff: Mentor

Magnets? What magnets?

Do you have an illustration of the apparatus?