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.
treverd
Messages
14
Reaction score
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.

 
Physics news on Phys.org
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!
 
Kindly see the attached pdf. My attempt to solve it, is in it. I'm wondering if my solution is right. My idea is this: At any point of time, the ball may be assumed to be at an incline which is at an angle of θ(kindly see both the pics in the pdf file). The value of θ will continuously change and so will the value of friction. I'm not able to figure out, why my solution is wrong, if it is wrong .
TL;DR Summary: I came across this question from a Sri Lankan A-level textbook. Question - An ice cube with a length of 10 cm is immersed in water at 0 °C. An observer observes the ice cube from the water, and it seems to be 7.75 cm long. If the refractive index of water is 4/3, find the height of the ice cube immersed in the water. I could not understand how the apparent height of the ice cube in the water depends on the height of the ice cube immersed in the water. Does anyone have an...
Back
Top