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dashkin111
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[SOLVED] Resonance (Differential Equations Class)
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?
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?
Homework Statement
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?
Homework Equations
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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