# Damped oscillation equation

1. The problem statement, all variables and given/known data
The equation for a damped oscillation is $$y(t)=Ae^{-\frac{b}{2m}t}cos(\omega’t + \phi)$$
We know that y(0)=0.5 and y'(0)=0.

Find the values of A and ø and then plot the oscillation in MATLAB.

2. Relevant equations
See above

3. The attempt at a solution
When derivating y(t) we get

$$y'(t)=Ae^{-\frac{b}{2m}t}(-\frac{b}{2m}cos(\omega’t+\phi)-\omega’sin(\omega’t + \phi))$$
This, together with the initial values gives that $$A=\frac{1}{2cos(\phi)}$$ and $$\phi=arctan(-\frac{b}{2m\omega’})$$

Is this correct? If not, then what is wrong?

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