Question

A sinusoidally carrying driving force is applied to a damped harmonic oscillator of force constant k and mass m. If the damping constant has a value b₁, the amplitude is A₁ when the driving angular frequency equals ?(k/m) . In terms of A₁, what is the amplitude for the same driving frequency and the same driving force amplitude F_max, if the damping constant is (a)3b₁ and (b)b₁/2? The oscillator is now at the resonace condition. If the damping constant b is halved, the amplitude at resonance would:

A) Stay the same

B) Increase by 4 times

C) Decrease by 4 times

D) Decrease by 2 times

E) None of the above

Answer 1

Here,

Hence the value of A becomes

Putting the value of omega in the above equation reduce the equation to

Now,

a) When 3b_1

Then

b) when b1/2