PHY354H1 Lecture Notes - Escape Velocity, Small-Angle Approximation, Becquerel
Document Summary
Lecture 20: energy and oscillations: relevant text sections: morin 5. 1-5. 2. Conservation of energy in one dimension: consider one dimensional motion under a force that is a function of x. In that case we can use our sneaky substitution trick from chapter 3 to remove time from the problem: We have (1: keep in mind that the velocity v = v(x). = m dv dt dv dx dx dt dv dx variables: (cid:90) v v0 (cid:90) x (cid:90) x x0 x0. F (x(cid:48))dx(cid:48) mvdv = f (x)dx mvdv = 0 : now we de ne a function v (x) such that. 1 we can nd v(x) for any f(x) using: (cid:90) x. F (x(cid:48))dx(cid:48) + v0, with v (x0) = v0 (2) x0. I can then isolate for the integral of f in this equation and plug it into my energy equation:
