Wednesday

July 23, 2014

July 23, 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)

**Related Questions**

Physics PLEASE - I'm trying to derive the formula v^2 = v0^2 + 2a(x-x0) were ...

AP Physics - I'm trying to derive the formula v^2 = v0^2 + 2a(x-x0) were zeros ...

PreCalculus REINY HELP PLEASE - well yay thanks for the answer but i really need...

physics - Please show me how to derive the relativist mass formula: m = m0 / ...

Chemistry - Derive a formula for the molar mass of the solute in terms of the ...

Physics - How would you derive the formula {-Ff+Fgx=ma} to show that µs=tanč

AP Physics - Hello I was trying to find the proof of the formula x = x0 + v0t +....

chemistry - Derive the empirical formula of a hydrocarbon that on analysis gave ...

Algebra - can show me how to do this with out just squaring 3x^(1/2) - x - 6 = 0...

Geometry - Please help! I'm really confused on what it is asking. Use the ...