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Theriot2
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A mass weighing 32 pounds stretches a spring 6 inches. The spring constant is equal to 64 lb/ft.The mass moves through a medium offering a damping force that is numerically equal to \beta times the instantaneous velocity. Determine the values of \beta>0 for which the spring/mass system will exhibit oscillatory motion.
2*\lambda=\frac{\beta}{m}
\omega^{2}=\frac{k}{m}
\lambda^{2} - \omega^{2}>0 is overdamped
\lambda^{2} - \omega^{2}=0 is critically damped
\lambda^{2} - \omega^{2}<0 is underdamped
1 slug = 32 pounds
I've solved that \beta is equal/less than/greater than 2*\sqrt{k*m}=32, but I don't understand when it will or will not have oscillatory motion.
2*\lambda=\frac{\beta}{m}
\omega^{2}=\frac{k}{m}
\lambda^{2} - \omega^{2}>0 is overdamped
\lambda^{2} - \omega^{2}=0 is critically damped
\lambda^{2} - \omega^{2}<0 is underdamped
1 slug = 32 pounds
I've solved that \beta is equal/less than/greater than 2*\sqrt{k*m}=32, but I don't understand when it will or will not have oscillatory motion.
