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Physics - Classical Mechanics

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A sinusoidally varying driving force is applied to a damped harmonic oscillator of force constant k and mass m. If the damping constant has a value b_1, the amplitude is A_1 when the driving angular frequency equals sqaureroot {k/m}.

a) In terms of A_1, what is the amplitude for the same driving frequency and the same driving force amplitude F_{max}, if the damping constant is 3b_{1}?

b) In terms of A_1, what is the amplitude for the same driving frequency and the same driving force amplitude F_{max}, if the damping constant is b_{1}/2?

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The general equation for one-dof forced vibration system is

m*x" + cx' + kx = F0*sin(w*t)

This is a second order ordinary differential equation. Its solution is x(t) = ...

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