Damped Oscillation with a Driving Force (Help)

In summary, for a damped harmonic oscillator with a sinusoidally varying driving force and a damping constant of b_1, the amplitude is A_1 when the driving angular frequency is equal to sqrt(k/m). When the damping constant is 3b, the amplitude is (1/3)A_1 for the same driving frequency and driving force amplitude F_{max}. When the damping constant is (1/2)b, the amplitude is 2A_1 for the same driving frequency and driving force amplitude F_{max}.
  • #1
treverd
14
0

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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  • #2
I got the answers they are

(1/3) A_1

and

2A_1
 
  • #3
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!
 

1. What is Damped Oscillation with a Driving Force?

Damped oscillation with a driving force is a phenomenon that occurs when a system undergoes periodic motion that is gradually reduced due to the presence of a damping force. The periodic motion is driven by an external force or input, known as the driving force.

2. How does Damped Oscillation with a Driving Force differ from Simple Harmonic Motion?

Damped oscillation with a driving force differs from simple harmonic motion in that it experiences a damping force, which causes the amplitude of the oscillations to decrease over time. This is in contrast to simple harmonic motion, which does not experience any damping and maintains a constant amplitude.

3. What factors affect the magnitude of the Damping Force in Damped Oscillation with a Driving Force?

The magnitude of the damping force in damped oscillation with a driving force is affected by several factors, including the velocity of the oscillating system, the properties of the damping material, and the frequency of the driving force. A higher velocity, higher damping coefficient, and higher frequency of the driving force will result in a larger damping force.

4. What is the relationship between the Damping Force and the Amplitude of Damped Oscillation with a Driving Force?

The damping force and the amplitude of damped oscillation with a driving force are inversely proportional. This means that as the damping force increases, the amplitude of the oscillations decreases. Conversely, a decrease in the damping force will result in an increase in the amplitude of the oscillations.

5. How is Damped Oscillation with a Driving Force used in real-world applications?

Damped oscillation with a driving force has a wide range of applications in various fields, including engineering, physics, and biology. Some examples include shock absorbers in vehicles, pendulum clocks, and the movement of cells in response to external stimuli. Understanding damped oscillations is crucial in designing and optimizing these systems for maximum efficiency and stability.

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