Physics

posted by Kim

I'm haivng troulbe proving the deriviation of this formula on my own...

could you please help me derive the proof of the formula or maybe show me one thansk...

I need to prove this formula

period of a mass spring system in simple harmonic motion

T = 2 pi square root of (m/k)
period = 2 pi X square root of (mass divided by spring constant)

thanks

1. Damon

F = m a
F = -k x for spring of constant k in N/m
so
m a = - k x
now assume motion of form x = A sin (2 pi f t)
then
dx/dt = velocity = A (2 pi f) cos 2 pi f t)
then
d velocity/dt = a = -A (2 pi f)^2 sin (2 pi f t)
or in other words
a = - x (2 pi f)^2
so
- k x = m [ - x (2 pi f)^2 ]
or
(2 pi f)^2 = k/m
so
2 pi f = sqrt (k/m)
but T = 1/f
so
T = 2 pi sqrt (m/k)

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