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

Click For Summary

Discussion Overview

The discussion revolves around modeling damped harmonic motion using the functions y=(e^ax) sin(bx) and y=(e^ax) cos(bx). Participants explore examples and applications of these functions in physical systems, particularly in relation to oscillatory motion.

Discussion Character

  • Exploratory
  • Technical explanation
  • Conceptual clarification
  • Debate/contested

Main Points Raised

  • One participant suggests using a simple pendulum as an example of damped harmonic motion but notes that y cannot represent both sine and cosine simultaneously.
  • Another participant proposes using a mass on the end of a spring and inquires about the graph's appearance.
  • Multiple examples of damped motion are mentioned, including a spring system, voltage across an RC oscillator, and electromagnetic waves in a lossy medium.
  • A participant requests clarification on the formula for damped motion on a spring, suggesting a form involving cosine and exponential decay.
  • There is a suggestion to refer to Wikipedia for additional information.
  • A later reply emphasizes the need for a "dashpot" to achieve damping in the spring system.
  • Another participant advises looking into the underdamping case in damped harmonic motion.

Areas of Agreement / Disagreement

Participants express various ideas and examples related to damped harmonic motion, but there is no consensus on a single model or example. The discussion remains open with multiple competing views and suggestions.

Contextual Notes

Some assumptions about the systems being modeled are not explicitly stated, and the discussion includes various interpretations of damping and oscillatory behavior without resolving the mathematical details.

Who May Find This Useful

Individuals interested in physics, particularly those studying oscillatory motion, damping effects, and mathematical modeling of physical systems.

botty_12
Messages
4
Reaction score
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?
 
Physics news on Phys.org
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.
 

Similar threads

Graduate Modeling the damping of a physical rigid pendulum
  • · Replies 1 ·
Replies
1
Views
2K
Undergrad Damped oscillator with changing mass
  • · Replies 131 ·
5
Replies
131
Views
9K
Graduate Queries on Damped Harmonic Motion
  • · Replies 2 ·
Replies
2
Views
2K
Undergrad Simple Harmonic Motion: why sin(wt) instead of sin(t)?
  • · Replies 3 ·
Replies
3
Views
8K
Zero Amplitude Damped Simple Harmonic Motion with k=0.7s^-1 and f=3Hz
  • · Replies 5 ·
Replies
5
Views
2K
Graduate Are harmonics "real" in a vibrating string?
  • · Replies 58 ·
2
Replies
58
Views
8K
Graduate Understanding Damped Harmonic Motion
  • · Replies 7 ·
Replies
7
Views
4K
Construction of a model of a hydraulic damper
  • · Replies 21 ·
Replies
21
Views
2K
Graduate Understanding Angular Displacement in Weakly Damped Harmonic Oscillators
  • · Replies 2 ·
Replies
2
Views
2K
Graduate Under-damped simple harmonic motion solution derivation
  • · Replies 5 ·
Replies
5
Views
3K