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clemente
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Homework Statement
A particle moves along x-axis subject to a force toward the origin proportional to -kx. Find kinetic (K) and potential (P) energy as functions of time t, and show that total energy is contant.
Homework Equations
K = (1/2)m*v^2
P = (1/2)k*x^2
E = K+P
x = Asin(wt + [tex]\tau[/tex])
v = dx/dt = wA(cos(wt + [tex]\tau[/tex])
The Attempt at a Solution
K = (1/2)m*v^2 = (1/2)m*w^2A^2(cos^2(wt + [tex]\tau[/tex])
P = (1/2)k*x^2 = (1/2)k*A^2(sin^2(wt + [tex]\tau[/tex]))
But when I add these to get the total energy, the terms with t do not cancel, and so the total energy is not constant. I can only imagine then that I've done something wrong in the above, very basic steps. Any suggestions would be appreciated. Thanks.