Simple Harmonic Motion, Initial Displacement vs Initial Cond

Click For Summary

Discussion Overview

The discussion revolves around the mathematics of simple harmonic motion, specifically addressing the initial displacement and conditions in a given example. Participants explore the implications of using different units and the interpretation of initial conditions in oscillatory motion.

Discussion Character

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

Main Points Raised

  • One participant questions why the initial condition for displacement is given as -1/2 when the object is initially displaced by 6 inches, suggesting a potential misunderstanding of the timing of t=0.
  • Another participant explains that the initial displacement can be considered as half the peak-to-peak amplitude, proposing that the author may be using a fractional representation for displacement.
  • There is a suggestion that the negative sign in the initial condition may indicate that the restoring force acts in the opposite direction to the displacement.
  • A participant expresses confusion about the calculation of amplitude being larger than the initial displacement, wondering if this is due to initial velocity and the object not starting from rest.
  • Some participants clarify that if imperial units are used, 6 inches corresponds to 1/2 a foot, which may affect calculations involving gravitational acceleration.

Areas of Agreement / Disagreement

Participants express differing views on the appropriateness of the initial displacement representation and the implications of using fractional units. The discussion remains unresolved regarding the clarity of the initial conditions and their interpretation.

Contextual Notes

There are limitations regarding the assumptions made about the timing of t=0 and the definitions of displacement and amplitude. The discussion also highlights potential confusion stemming from the use of imperial units in calculations.

austrosam
Messages
5
Reaction score
0
Hi everybody,

I'm writing an exploration on the mathematics of simple harmonic motion and I stumbled across something I fail to understand in one of my resources (http://tutorial.math.lamar.edu/Classes/DE/Vibrations.aspx). In the example the author uses toward the end of the resource, the object is initially displaced by 6 inches (don't ask me why he felt the need to use imperial units) but then, the initial condition for displacement given at t=0 is -1/2. Should it not be 6?

My guess is that one can simply set t=0 at any point during the oscillation and not in fact when the oscillation is started, but that still would not quite explain everything. Maybe I am just being very silly...

Many thanks for any advice!

Sam
 
Physics news on Phys.org
If you pull a pendulum to one side by 6" and let it go it will swing back and forth a total distance of 12". So the initial displacement is half the peak to peak amplitude. It sounds like they decided to use "fraction of peak to peak amplitude" as the unit of displacement rather than inches or meters.

The minus sign is probably because the restoring force is in the opposite direction to the displacement.
 
CWatters said:
If you pull a pendulum to one side by 6" and let it go it will swing back and forth a total distance of 12". So the initial displacement is half the peak to peak amplitude. It sounds like they decided to use "fraction of peak to peak amplitude" as the unit of displacement rather than inches or meters.

The minus sign is probably because the restoring force is in the opposite direction to the displacement.
Right, I guess that makes sense, though I must say it still seems a little odd, to me it would seem much more straightforward to use a value of 6 inches instead.

Many thanks anyway!

One more thing, I merely need quick confirmation I'm on the right track here. Later on, they calculated the amplitude which was slightly larger than the initial displacement. Is this because of the initial velocity, and the object not starting from rest?
 
I f the author is using imperial units then the lengths would be in feet - so 6 inches is 1/2 a foot. Then they would use g=32 ft/sec/sec.
 
bhillyard said:
I f the author is using imperial units then the lengths would be in feet - so 6 inches is 1/2 a foot. Then they would use g=32 ft/sec/sec.

Perfect! Thank you! I am totally unfamiliar with imperial units, I should have really checked that. Thanks!
 

Similar threads

High School Is simple harmonic motion also a pure translatory motion?
  • · Replies 21 ·
Replies
21
Views
3K
Undergrad Solutions to Simple Harmonic Motion second order differential equation
  • · Replies 1 ·
Replies
1
Views
1K
Undergrad Angular Velocity in Simple Harmonic Motion
  • · Replies 11 ·
Replies
11
Views
16K
Undergrad Simple Harmonic Motion: why sin(wt) instead of sin(t)?
  • · Replies 3 ·
Replies
3
Views
8K
Undergrad Simple Harmonic Motion: conceptual idea of angular frequency
  • · Replies 2 ·
Replies
2
Views
2K
Graduate Supressed harmonics with certain initial conditions
  • · Replies 1 ·
Replies
1
Views
2K
Graduate Damped Harmonic Oscillator - Gravity not constant.
  • · Replies 9 ·
Replies
9
Views
3K
Undergrad Is a Vertically Hung Spring Mass System SHM?
  • · Replies 8 ·
Replies
8
Views
2K
Undergrad Phase constant in simple harmonic motion
  • · Replies 3 ·
Replies
3
Views
9K
How to prove that motion is periodic but not simple harmonic?
  • · Replies 51 ·
2
Replies
51
Views
4K