Answer:
f = 7.57 Hz
Explanation:
To find the frequency of the damping oscillator, you first use the following formula for the angular frequency:
[tex]\omega=\sqrt{\omega_o-(\frac{b}{2m})^2}=\sqrt{\frac{k}{m}-(\frac{b}{2m})^2}\\\\[/tex] Â (1)
k: spring constant = 2.65*10^4 N/m
m: Â mass = 11.7 kg
b: damping coefficient = 4.50 Ns/m
You replace the values of k, m and b in the equation (1):
[tex]\omega=\sqrt{\frac{2.65*10^4N/m}{11.7kg}-(\frac{4.50Ns/m}{2(11.7kg)})^2}\\\\\omega=47.59\frac{rad}{s}[/tex]
Finally, you calculate the frequency:
[tex]f=\frac{\omega}{2\pi}=\frac{47.59}{2\pi}Hz=7.57\ Hz[/tex]
hence, the frequency of the oscillator is 7.57 Hz
