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Eric_meyers
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Homework Statement
"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. "
Homework Equations
f = -kx
w = (k/m)^1/2
frequency = w/(2 * pi)
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.