Does the derivation of the SHM formula require calculus?

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Discussion Overview

The discussion revolves around the derivation of the simple harmonic motion (SHM) formula and whether it necessitates the use of calculus. Participants explore different methods of derivation, including algebraic and trigonometric approaches, as well as connections to circular motion.

Discussion Character

  • Exploratory, Technical explanation, Debate/contested

Main Points Raised

  • One participant expresses interest in deriving the SHM formula independently and questions if it can be done without calculus.
  • Another participant asks for clarification on which specific SHM equation is being considered for derivation.
  • It is noted that SHM can be viewed as the projection of circular motion.
  • One participant argues that a proper derivation requires calculus, citing Newton's second law (F=ma) and a simple differential equation.
  • A different participant claims to have derived SHM from circular motion without calculus, highlighting the relationship between centripetal force and displacement.

Areas of Agreement / Disagreement

Participants express differing views on the necessity of calculus for deriving the SHM formula. Some believe calculus is essential, while others argue that it can be derived using algebra and trigonometry.

Contextual Notes

Participants reference different methods and perspectives on derivation, indicating a lack of consensus on the approach required for deriving the SHM formula.

Elbobo
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It's not a homework question, but I wanted to attempt to derive it on my own. I was lookin for some clues online, and I believe I saw a website using derivatives.

Can it be done using pure algebra and trigonometry?
 
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There are a number of equations that apply to simple harmonic motion. Which one are you thinking of? And what do you want to derive it from?
 
yes,shm is equivalent to the projection of circular motion
 
Yes and no.

The "real" way, in my mind, does require calculus. I consider it the real way because it comes directly from F=ma. The calculus isn't that tough, though, its a pretty simple differential equation that says that m x == m x''.

What kof refers to is this:

http://img229.imageshack.us/img229/8670/demodt0.gif

If you were to follow the path of a mass tracing out uniform circular motion, then the projection of the mass's x position would mimic that of a harmonic oscillator on the end of a spring.

Describing the position of the mass in terms of theta, then you can see that the harmonic oscillator equation works.
 
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yeah,that's what i mean,in circular motion with constant speed,you can prove the x-component of centripetal force is proportional to the displacement along x-axis,with an opposite direction,i derived shm this way before i learned calculus
 

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