- #1

Redwaves

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- 7

- 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.