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Remark about E(t)

E(t) does not measure energy, energy per mass unit.

Starting with an ODE coming directly from Newton's 2nd law F=ma with a spring force F=ku and ma=mu (a: acceleration, u: displacement), we have

mu+ku=0 Integrating this equation gives a physical energy balance:

E(t)=12mv2kinetic energy+12ku2potential energy=E(0),v=u Note: the balance is not valid if we add other terms to the ODE.

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