- #1
cj
- 85
- 0
For a simple damped oscillator...
[tex] \text {Apparently if } \beta \ll \omega_0 } \text { then ...}[/tex]
[tex] \omega_d \approx \omega_0[1-\frac {1}{2}(\beta/\omega_0)^2]}[/tex]
Given that:
[tex] \beta=R_m/2m \text { (where } R_m= \text {mechanical resistance) } \text { and } \omega _d=\sqrt{(\omega _0^2-\beta ^2)}[/tex]
How/why is this true? My guess is some kind of
series approximation is used -- but I'm not sure...
[tex] \text {Apparently if } \beta \ll \omega_0 } \text { then ...}[/tex]
[tex] \omega_d \approx \omega_0[1-\frac {1}{2}(\beta/\omega_0)^2]}[/tex]
Given that:
[tex] \beta=R_m/2m \text { (where } R_m= \text {mechanical resistance) } \text { and } \omega _d=\sqrt{(\omega _0^2-\beta ^2)}[/tex]
How/why is this true? My guess is some kind of
series approximation is used -- but I'm not sure...