Damped oscillations - Finding damping coefficient

In summary, a damped oscillation is a type of periodic motion where the amplitude decreases over time due to external forces. The damping coefficient is calculated by measuring the amplitude over time and is affected by factors such as damping force, mass, and stiffness. It is important because it quantifies energy dissipation and is used in various applications to model and analyze damped oscillating systems.
  • #1
diffusion
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Homework Statement


A 50.0g hard-boiled egg moves on the end of a spring with force constant k = 25.0 N/m. It is released with an amplitude 0.300m. A damping force Fx = -bv acts on the egg. After it oscillates for 5.00s, the amplitude of the motion has decreased to 0.100m.
Calculate the magnitude of the damping coefficient b.

Homework Equations


render?tex=x+%3D+Ae%5E%7B-bt%2F2m%7D%5Ccos%7B%28%5Comega+%27t%2B%5Cphi+%29%7D.gif



The Attempt at a Solution


I honestly have no idea how to approach this question. Could someone steer me in the right direction?
 
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  • #2
Anyone?
 
  • #3
diffusion said:

Homework Equations


render?tex=x+%3D+Ae%5E%7B-bt%2F2m%7D%5Ccos%7B%28%5Comega+%27t%2B%5Cphi+%29%7D.gif

Note that the amplitude, at time t, is given by


Amplitude = A e-bt/2m
​
 

1. What is a damped oscillation?

A damped oscillation is a type of periodic motion where the amplitude of the oscillation decreases over time due to the presence of an external force or energy dissipation.

2. How is the damping coefficient calculated?

The damping coefficient can be calculated by measuring the amplitude of the oscillation over time and using a mathematical equation to determine the rate of decrease in amplitude.

3. What factors affect the damping coefficient?

The damping coefficient can be affected by the type and strength of the damping force, the mass and stiffness of the oscillating system, and any external factors that may influence the motion.

4. Why is the damping coefficient important?

The damping coefficient is important because it helps to quantify the amount of energy dissipation in a damped oscillation, which can affect the overall behavior and stability of a system.

5. How is the damping coefficient used in real-world applications?

The damping coefficient is used in various fields such as engineering, physics, and acoustics to model and analyze the behavior of damped oscillating systems, such as in shock absorbers, musical instruments, and electrical circuits.

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