Simple Harmonic Motion

[thais]

How is the force of a spring related to Amplitude besides E = kA^2/2

I've seen in a couple places now that F=kA .
How do we derive that? Is it from the formula x = Acos( wt +angle )? And most importantly, do we need to know this formula for the MCAT?

Thank you!

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[MedPR]

How is the force of a spring related to Amplitude besides E = kA^2/2

I've seen in a couple places now that F=kA .
How do we derive that? Is it from the formula x = Acos( wt +angle )? And most importantly, do we need to know this formula for the MCAT?

Thank you!

F=kx is the equation for a spring. A is just amplitude, which is displacement, which is x.

 

[milski]

From f=ma and f=kx you can write a differential equation relating m, a, k and x. Solving that gives you x = A cos(...) etc. You can differentiate that and find the velocity. From there the energy is just mv^2/2. You need to know them for simple harmonic motion problems but you don't need to know how to derive them.

 

[thais]

thanks guys!