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

• botty_12
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.
botty_12
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?

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)

Would i be able to use a mass on the end of a spring? what would the graph look like if so?

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.

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)

Try wikipedia

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.

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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