 #1
Redwaves
 134
 6
 Homework Statement:
 Finding the amplitude of a driven oscillator
 Relevant Equations:

Oscillator without driven force at ##t_0##, ##x(t_0) = 5.0e^{7t_0} cos (24t_0 + \frac{\pi}{4})##
at ##t_2## an external force is applied
Force, ##F(t_2) = 35.0sin(25t_2 + \frac{\pi}{3})##
m = 2.5kg
I found ## \frac{\gamma}{2} = 7##, ##\gamma = 14##
##\omega_0^2 = \omega_d^2 + \frac{\gamma^2}{4} = 25##
##\omega_0 = \omega = 25##, thus ##\delta = \frac{\pi}{2}##
##A = \frac{\frac{F_0}{m}}{\sqrt((\omega_0^2  \omega^2)+ \gamma^2\omega^2)} = 0.04##
Thus, ##X(t) = 0.04sin(25t + \frac{\pi}{3}  \frac{\pi}{2})##
However, the correct answer in my book is
##X(t) = 4sin(25t + \frac{4\pi}{3})##
I don't see why my amplitude and the phase isn't correct.
##\omega_0^2 = \omega_d^2 + \frac{\gamma^2}{4} = 25##
##\omega_0 = \omega = 25##, thus ##\delta = \frac{\pi}{2}##
##A = \frac{\frac{F_0}{m}}{\sqrt((\omega_0^2  \omega^2)+ \gamma^2\omega^2)} = 0.04##
Thus, ##X(t) = 0.04sin(25t + \frac{\pi}{3}  \frac{\pi}{2})##
However, the correct answer in my book is
##X(t) = 4sin(25t + \frac{4\pi}{3})##
I don't see why my amplitude and the phase isn't correct.