Damped harmonic oscillator Definition and 52 Threads

For a simple damped oscillator... \text {Apparently if } \beta \ll \omega_0 } \text { then ...} \omega_d \approx \omega_0[1-\frac {1}{2}(\beta/\omega_0)^2]} Given that: \beta=R_m/2m \text { (where } R_m= \text {mechanical resistance) } \text { and } \omega _d=\sqrt{(\omega...

Question: A damped harmonic oscillar loses 5.0 percent of its mechanical energy per cycle. (a) By what percentage does its frequency differ from the natural frequency \omega_0 = \sqrt{k/m}? (b) After how many periods will the amplitude have decreased to 1/e of its original value? (a) Let E(t)...