PHY354H1 Lecture Notes - Exponential Decay, Damping Ratio, Step Function
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I won"t go through this section in lecture, but i thought it might be nice to have a recap in your notes. The lecture will begin at the lecture starts. So far, we have been studying f = m x for a variety of forces. I recap the main equations and results below: restoring forces only, examples: springs: f = kx, small angle pendulums: f = Mgx/l (where x is the angle): equation we solve: 0x = 0 where 0 is the natural frequency of the oscillations and is given by the square root of the coe cient in front of the x in the forcing k/m, in divided by mass. 0x = 0 where = b/2m: the solution depends on the relative magnitudes of and 0. There are 3 cases: (a) underdamped: 2 < 2 (b) overdamped: 2 > 2. 0 2 is real and so we get oscillations that.
