Understanding Simple Harmonic Motion: The Role of Frequency in Wave Equations

Click For Summary

Discussion Overview

The discussion revolves around the derivation of simple harmonic motion (SHM) equations, specifically focusing on the role of frequency as a constant in the equations. Participants explore the relationship between force, displacement, and frequency in the context of SHM, particularly for a pendulum system.

Discussion Character

  • Exploratory
  • Technical explanation
  • Debate/contested

Main Points Raised

  • One participant questions whether there is a derivation that shows the constant in the SHM equation is the frequency of SHM.
  • Another participant emphasizes that the basis of SHM is that the restoring force is proportional to the displacement, acting in the opposite direction.
  • A participant specifies that the system in question is a pendulum.
  • One participant suggests that SHM equations could be derived using the principle of conservation of mechanical energy.
  • Another participant states that the constant in the equation cannot be the frequency itself, but for a unit mass system, it is equal to the frequency squared.
  • There is a request for clarification on the definition of SHM being used, with one participant admitting they have not studied a formal definition but are aware of properties like the restoring force.

Areas of Agreement / Disagreement

Participants express differing views on the relationship between the constant in the SHM equation and frequency, with some asserting that the constant cannot be frequency itself, while others seek clarification on the derivation and definitions involved. The discussion remains unresolved regarding the specific derivation linking the constant to frequency.

Contextual Notes

There are limitations regarding the definitions of SHM being used and the assumptions about the systems being discussed, particularly concerning the role of mass in the equations.

Shan K
Messages
73
Reaction score
0
I was reading a book on wave and found that when they derive the equation of shm from the equation force varies with negetive displacement , they had taken a propotionality constant to make the force and displacement equal and they had taken frequency of the shm as the constant . So my question is , is there any derivation which can show that the constant is the frequency of the shm .
 
Physics news on Phys.org
It would help if you told us what the system was.
Spring and mass vertical or horizontal?
Pendulum?
?

The basis of SHM is always that the restoring force is proportional to the displacement (from the mean position). Since the force tends to return the system to the mean position is acts in the opposite direction to the displacement so one is negative.
 
It was for pendulum
 
I am not sure what your question is; anyway, the equations of shm could be derived by applying the principle of conservation of mechanical energy.
 
Let me show u the derivation .
We know that for shm


force varies as negetive displacement


therefore,
force equal to some constant times negetive displacement


they said that this constant is equal to the frequency of the shm . I want to know how ?
( sorry for writing all the equation in words cus my mobile doesn't support to write equations with some special charecters . )
 
Sorry to ask another question but I don't want to post something different from your course.

What definition of SHM are you using?
 
Shan K said:
So my question is , is there any derivation which can show that the constant is the frequency of the shm .

No, because the units mean that can't possibly be correct.

But for a system with unit mass, the constant is equal to the frequency squared (frequency measured in radians/second, not Hz).

This should be explained in any textbook or website about the dynamics of single degree of freedom (SDOF) systems.

For a pendulum, the "unit mass" part doesn't matter, since the force (i.e. weight) is proportional to the mass.
 
Studiot said:
Sorry to ask another question but I don't want to post something different from your course.

What definition of SHM are you using?

i don't have studied any kind of definition on shm . What i have studied is some properties of that like it has a restoring force
 

Similar threads

Undergrad The speed of a waves on a string in Simple harmonic motion
  • · Replies 8 ·
Replies
8
Views
3K
Undergrad Solutions to Simple Harmonic Motion second order differential equation
  • · Replies 1 ·
Replies
1
Views
1K
Undergrad Simple Harmonic Motion: conceptual idea of angular frequency
  • · Replies 2 ·
Replies
2
Views
2K
Undergrad Angular Velocity in Simple Harmonic Motion
  • · Replies 11 ·
Replies
11
Views
16K
Undergrad Is a Vertically Hung Spring Mass System SHM?
  • · Replies 8 ·
Replies
8
Views
2K
Undergrad Simple Harmonic Motion: why sin(wt) instead of sin(t)?
  • · Replies 3 ·
Replies
3
Views
8K
Undergrad Equation for Simple Harmonic Motion?
  • · Replies 6 ·
Replies
6
Views
6K
Undergrad Find Frequency of Block Oscillation Due to Shear Force
  • · Replies 1 ·
Replies
1
Views
2K
Undergrad Phase constant in simple harmonic motion
  • · Replies 3 ·
Replies
3
Views
9K
High School Phase angle and Phase in Simple harmonic motion
  • · Replies 7 ·
Replies
7
Views
2K