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December 21, 2014

December 21, 2014

Posted by **Kim** on Saturday, May 30, 2009 at 12:52pm.

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

- Physics -
**Damon**, Saturday, May 30, 2009 at 1:28pmF = 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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