Originally Posted by

**purakanui** I am stuck on this question, I have done a little but I am generally lost. The second order equation is the general form of modeling springs (g is for gamma, but g is easier to type)

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Show that the solution of the initial value problem

my'' + gy' + ky = 0, y(t0) = y0, y'(t0) = y1

can be expressed as the sum y = v + w, where v satisfies the initial conditions

v(t0) = y0, v'(t0) = 0

w satisfies the initial conditions

w(t0) = 0, w'(t0) = y1

and both v and w satisfy the same differential equation as u.

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