Damped harmonic oscillator physics

In summary, the conversation discusses a driven damped harmonic oscillator and the calculation of power dissipated by the damping force. The differential equation for a damped harmonic oscillator is compared to that of a normal harmonic oscillator, with the difference being the diminishing amplitude as time changes. The conversation ends with a request for help on the problem.
  • #1
brad sue
281
0
Please I don't understand this problem at all:

Consider a driven damped harmonic oscillator.Calculate the power dissipated by the damping force?
calculate the average power loss, using the fact that the average of (sin(wt+phi) )^2 over a cycle is one half?

Please can I have some help for it?

B
 
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  • #2
Well, what's the differential equation which describes a damped harmonic oscillator? How does this differ from the normal harmonic oscillator equation? What, physically, causes this difference?
 
  • #3
dicerandom said:
Well, what's the differential equation which describes a damped harmonic oscillator? How does this differ from the normal harmonic oscillator equation? What, physically, causes this difference?
I know that x(t)= A*exp(alpha*t) *sin(wt+phi)
the diffierence come from the fact that the amplitude diminishes as t changes.
 

FAQ: Damped harmonic oscillator physics

What is a damped harmonic oscillator?

A damped harmonic oscillator is a type of physical system that exhibits oscillatory motion, where the amplitude of the oscillations decreases over time due to the presence of a damping force. This damping force can come from friction, air resistance, or other external factors.

How does a damped harmonic oscillator differ from an undamped harmonic oscillator?

An undamped harmonic oscillator is a system that exhibits oscillatory motion without any external forces causing the amplitude of the oscillations to decrease. In contrast, a damped harmonic oscillator has an additional damping force that causes the amplitude to decrease over time.

What is the equation of motion for a damped harmonic oscillator?

The equation of motion for a damped harmonic oscillator is given by:

m * d^2x/dt^2 + b * dx/dt + k * x = 0

Where m is the mass of the oscillator, b is the damping coefficient, k is the spring constant, and x is the displacement of the oscillator from its equilibrium position.

How does the damping coefficient affect the behavior of a damped harmonic oscillator?

The damping coefficient, b, determines the strength of the damping force acting on the oscillator. A larger damping coefficient will result in a faster decrease in amplitude of the oscillations, leading to a shorter oscillation period and a smaller maximum displacement. A smaller damping coefficient will result in slower decrease in amplitude, leading to a longer oscillation period and a larger maximum displacement.

What are some real-life examples of damped harmonic oscillators?

Damped harmonic oscillators can be found in many everyday objects, such as a swinging pendulum, a car suspension system, a guitar string, or even the vibrations of a building during an earthquake. They are also used in many mechanical and electrical systems to control and reduce vibrations.

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