Please anser all the above ecpicailly from c to H thank you Consider a damped dr

Question

Please anser all the above ecpicailly from c to H

thank you

Consider a damped driven oscillator with the following parameters: s = 200 N/m m = 0.05kg b = 0.8 kg/s F_0 = 10N A) Find the resonant frequency, omega. B) Find the damping rate gamma. C) Hat is the quality factor Q for this oscillator? D) Is this oscillator lightly damped, critically damped, or heavily damped? E) Find the steady state amplitude when the oscillator is driven on resonance (Ohm = omega). F) Find the steady state amplitude when Ohm = omega + gamma/2. G) Find the average power delivered to the oscillator when the oscillator is driven on resonance (Ohm = omega). H) Find the average power delivered to the oscillator when Ohm = omega + gamma/2.

Explanation / Answer

given

s = 200 N/m

m = 0.05 kg

b = 0.8 kg/s

Fo = 10 N

A) resontnat frequency , wo = sqroot(s/m) = sqroot(200/0.05) = 63.24 rad/s

B) damping rate, gamma = b/2m = 0.8/2*0.05 = 8 / s

C) Quality factor, Q = sqroot(ms)/b = sqroot(0.05*200)/0.8 = 3.952

Q > 0.5, underdamped system

D) b^2 - 4*ms = 0.8^2 - 4*0.05*200 = -39.36 < 0

so this osscilator is underdamped

E) steady state ampliyude when wo = w

A = Fo/m*sqroot([wo - w]^2 + 4 *gamma^2*w^2)

A = 10/0.05*2*8*63.24 = 0.19765 m

F) when w = wo + gamma/2

A = Fo/m*sqroot([wo - w]^2 + 4 *gamma^2*w^2)

A = 10/0.05*sqroot((4)^2 + 4*64*(63.24 + 4)^2)

A = 0.185 m

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