Damped Oscillation with a Driving Force (Help)

AI Thread Summary
A damped harmonic oscillator is analyzed under a sinusoidal driving force, with specific focus on how varying the damping constant affects amplitude. When the damping constant is tripled, the amplitude is calculated to be (1/3) A_1, while reducing the damping constant to half results in an amplitude of 2A_1. The correct application of the formula A = (Fmax / sqrt((k - mw^2)^2 + (b^2 w^2))) is crucial for these calculations. The initial confusion regarding the answers was resolved after further clarification of the calculations. This discussion highlights the importance of showing work in problem-solving to identify errors.
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Homework Statement


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 sqrt (k/m).

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?

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 (1/2)b?

Homework Equations


A= (Fmax/(sqrt(k-mw^2)^2+(b^2w^2))

w= omega


The Attempt at a Solution


I try to put in the the b values but it is saying it is incorrect.

 
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I got the answers they are

(1/3) A_1

and

2A_1
 
Where is your work? How can I know what you did wrong if you don't show me your work?

EDIT: I see you figured it out. Good Job!
 
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