A mass is oscillating on a spring with simple harmonic motion. Its amplitude is 0.80m and its maximum speed is 1.5m/s, at the point of equilibrium. What is the speed of the mass at 0.60m?
Is there enough information to answer this question? The answer given is 0.75m/s, but I can't figure out how to get there.
Ep = kx2/2
Ec = mv2/2
Em = Ep + Ec
The Attempt at a Solution
I've made many attempts at this, all completely wrong. I always end up trying to factorize (my teacher told us that the answer involves factorizing) but it goes absolutely haywire.
Em = Em'
Epmax = Ecmax
kxmax2/2 = mvmax2/2 (the 1/2 cancels for each formula)
vmax/xmax = √k/m (which should be constant)
(1,5m/s)2/(0.80m)2 = √k/m
1.875(not sure what unit to put here) = √k/m ∴ k/m = 3.516
kx2 + mv2 = mvmax2 (again the 1/2 cancels)
mvmax2 - mv2 = kx2
m(vmax2 - v2) = kx2
vmax2 - v2 = kx2/m
k/m = (vmax2 - v2)/x2
If the k/m stays constant, which I believe it should, it should be an easy substitution to find the v I'm looking for.
After manipulating the formula I got, I'm left with
v = √-(k/m - vmax2/x2)(x2)
After substituting, I get 0.99m/s.