(adsbygoogle = window.adsbygoogle || []).push({}); 1. The problem statement, all variables and given/known data

"Two light springs have spring constants k1 and k2, respectively, and are used

in a vertical orientation to support an object of mass m. Show that the angular

frequency of small amplitude oscillations about the equilibrium state is

[(k1 + k2)/m]^1/2 if the springs are in parallel, and [k1 k2/(k1 + k2)m]^1/2 if

the springs are in series. "

2. Relevant equations

f = -kx

w = (k/m)^1/2

frequency = w/(2 * pi)

3. The attempt at a solution

So I set up my fnet for the parallel one

m * x'' = - (k1x + k2x) since in the parallel feature there are two distinct springs exerting two distinct forces

however dividing through I'm left with

x'' = - (k1x + k2x)/m

I'm not quite sure how to use x'' to get to angular frequency or how to remove the negative sign.

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# Simple harmonic motion

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