Question

A point performs damped oscillations with frequency ω and damping coefficient β according to the law (4.1b). Find the initial amplitude a0 and the initial phase α if at the moment t = 0 the displacement of the point and its velocity projection are equal to

(a) x (0) = 0 and vx (0) =

(b) x (0) = x0 and vx (0) = 0.

Answer 1

Since a0 is + ve, we must choose the upper sign if and the lower sign if Thus