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1. The problem statement, all variables and given/known data

A front-loading washing machine is mounted on a thick rubber pad that acts like a spring; the weight W = mg (with g = 9.8 m/s^2) of the machine depresses the pad exactly 0.38 cm. When its rotor spins at \omega radians per second, the rotor exerts a vertical force

F_0 cos(omega t)

Newtons on the machine. Neglecting friction, determine at what speed (in revolutions per minute) resonance vibrations will occur?

2. Relevant equations

3. The attempt at a solution

I decided to just set it up like a force equation in physics.

[tex]

F=ma[/tex]

[tex]

kx=mg

[/tex]

Now solve for [tex]\omega[/tex] which is [tex]\sqrt{\frac{k}{m}}[/tex]

[tex]\frac{k}{m}=\frac{g}{x}=\omega^{2}[/tex]

So omega is:

[tex]\frac{35\sqrt{10}}{2}[/tex]

Transform to rpms

[tex]RPMS = \omega \frac{(60)}{2\pi}[/tex]

Which to the nearest RPM is 528. But this is wrong. Any clues?

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# Homework Help: Resonance (Differential Equations Class)

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