Model Damped Harmonic Motion with Y=(e^ax) Sin/Cos bx

In summary, the conversation discusses the use of the functions y=(e^ax) sin bx and y=(e^ax) cos bx in modeling various scenarios, including damped harmonic motion, a mass on a spring, voltage across an RC oscillator, electromagnetic waves, and particles in a finite well. The conversation also mentions the need for a "dashpot" for damping in a mass-spring system and suggests looking for the underdampening case in damped harmonic motion.
  • #1
botty_12
4
0
Hey guys, using my knowledge of y=(e^ax) sin bx and y=(e^ax) cos bx, I need to find an example where these functions could be used as a model. I was thinking about damped harmonic motion but had a tough time trying to find an example and how i could relate it to those two graphs, any ideas?
 
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  • #2
The example can be a simple pendulum. But "y" cannot be the two things simultaneously. It is sin or cos or more general: cos(bx+phi)
 
  • #3
Would i be able to use a mass on the end of a spring? what would the graph look like if so?
 
  • #4
Damped motion on a spring, voltage across an RC oscillator, an electromagnetic plane wave propagating through a lossy (or gain) medium, the tail of the wavefunction of a particle in a finite well: the list goes on and on and on.
 
  • #5
Could i please have a quick explanation of the damped motion on a spring, and will the graph have a formula something like y=(Ae^-ax) cox (bx+pi)
 
  • #6
Try wikipedia
 
  • #7
botty_12 said:
Would i be able to use a mass on the end of a spring? what would the graph look like if so?

you'ld need a "dashpot" for there to be any damping.
 
  • #8
Look for the underdampening case in damped harmonic motion.
 

What is the equation for damped harmonic motion?

The equation for damped harmonic motion is Y=(e^ax) Sin/Cos bx, where Y is the displacement of the object, e is the base of the natural logarithm, a is the damping coefficient, x is the time, Sin/Cos is either sine or cosine function, and b is the frequency of oscillation.

What does the damping coefficient represent in damped harmonic motion?

The damping coefficient, a, represents the rate at which the amplitude of the oscillations decreases over time. It is a measure of the amount of energy lost due to friction or other resistive forces.

How does the frequency of oscillation affect damped harmonic motion?

The frequency of oscillation, b, determines the rate at which the object vibrates. A higher frequency means the object will oscillate more times in a given time period, leading to a faster decrease in amplitude due to damping.

What is the difference between damped and undamped harmonic motion?

In damped harmonic motion, the amplitude of the oscillations decreases over time due to the presence of a damping force. In undamped harmonic motion, there is no damping force and the amplitude remains constant. However, both types of motion follow the same basic equation: Y=(e^ax) Sin/Cos bx.

How does the initial displacement and velocity affect damped harmonic motion?

The initial displacement and velocity of the object affect the amplitude and phase of the damped harmonic motion. A larger initial displacement will result in a larger amplitude, while a larger initial velocity will result in a larger phase shift. These initial conditions can greatly impact the behavior of the system over time.

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