Does the derivation of the SHM formula require calculus?

[Elbobo]

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?

 

[jtbell]

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?

 

[kof9595995]

yes,shm is equivalent to the projection of circular motion

 

[hbweb500]

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.

 

[kof9595995]

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