Damped Oscillation with a Driving Force (Help)

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SUMMARY

The discussion focuses on the behavior of a damped harmonic oscillator subjected to a sinusoidal driving force. The amplitude of oscillation is derived based on varying damping constants. Specifically, when the damping constant is three times the original value (3b), the amplitude is (1/3) A_1. Conversely, with a damping constant of (1/2)b, the amplitude increases to 2A_1. The relationship between damping, driving force, and amplitude is clearly established through the equation A = (Fmax / sqrt(k - mw^2)^2 + (b^2w^2)).

PREREQUISITES
  • Understanding of damped harmonic motion
  • Familiarity with the equation of motion for oscillators
  • Knowledge of sinusoidal functions and angular frequency
  • Basic grasp of force constants and damping coefficients
NEXT STEPS
  • Study the effects of varying damping constants on oscillation amplitude
  • Explore the derivation of the amplitude equation A = (Fmax / sqrt(k - mw^2)^2 + (b^2w^2))
  • Investigate the physical significance of the damping ratio in oscillatory systems
  • Learn about the implications of driving frequency on resonance in damped systems
USEFUL FOR

Students studying physics, particularly those focusing on mechanics and oscillatory motion, as well as educators seeking to explain the principles of damped oscillation and driving forces.

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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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