Underdamped oscillation

In summary, underdamped oscillation is a type of oscillatory motion where the restoring force is greater than the damping force, resulting in decreasing amplitude over time. It differs from overdamped oscillation in that the damping force is less than the critical damping value, and it can be observed in nature through examples such as pendulum motion and guitar string vibrations. The frequency of underdamped oscillation is affected by factors such as mass, spring constant, and damping coefficient, and it is used in real-world applications like shock absorbers and suspension systems.
  • #1
esradw
26
0
An underdamped oscillator`s amplitude decreases with the factor of e^-beta*T(damped) in a one cycle, but I am confused how to find the decrease of the amplitude after 10 cycles. Schould I multiply the factor by 10 like (10*e^-beta*T(damped) ) or when I am calculating the factor , should I just multiply the Td by 10 and then find the factor.( e^-beta*10*T(damped) ?
thanks
 
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  • #2
You should do [tex] e^{-10 \beta T} [/tex] where T is the time of one oscillation. I think.
 
  • #3
thanks that was what I thought to but I wasnt sure
 

1. What is underdamped oscillation?

Underdamped oscillation is a type of oscillatory motion in which the restoring force is greater than the damping force. This results in the oscillation having a decreasing amplitude over time.

2. How does underdamped oscillation differ from overdamped oscillation?

In underdamped oscillation, the damping force is less than the critical damping value, resulting in oscillations with a decreasing amplitude. In overdamped oscillation, the damping force is greater than the critical damping value, resulting in oscillations that decay to equilibrium without any oscillation.

3. What factors affect the frequency of underdamped oscillation?

The frequency of underdamped oscillation is affected by the mass of the object, the spring constant of the system, and the damping coefficient. A higher mass or spring constant will result in a lower frequency, while a higher damping coefficient will decrease the frequency.

4. How is underdamped oscillation used in real-world applications?

Underdamped oscillation is used in various real-world applications, such as in shock absorbers for vehicles, suspension systems for bridges, and in electronic circuits for filtering signals.

5. Can underdamped oscillation be observed in nature?

Yes, underdamped oscillation can be observed in nature. Examples include the motion of a pendulum, the swinging of a tree branch, and the vibrations of a guitar string.

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