1. ## function question

thanks skeeter

2. Originally Posted by captain_jonno
A boat is hit by a wave and oscillates 5.2 deg on either side of upright. If the ship is leaning 2.6 deg to the left and moving toward upright at t=0, write a function describing the lean angle, theta, as a function of time. Period of boats roll is 30sec.
see attached graph ...

3. hey skeeter i dont actually need the graph, but the working out to get to that point. If you know how?

plus when i plug that equation into my ti-83 the graph doesnt look the same.

your using a mac program for that right?

4. my mistake ... I misread the 5.2 degrees "either side" as the total oscillation.

General form for the equation that models this motion will be

$\displaystyle y = A\cos(\omega t + \delta)$

period = $\displaystyle T = 30 \, sec \, = \frac{2\pi}{\omega}$

$\displaystyle \omega = \frac{\pi}{15}$

$\displaystyle A = -5.2$

at this point ...

$\displaystyle y = -5.2\cos\left(\frac{\pi}{15} t + \delta\right)$

at $\displaystyle t = 0$ , $\displaystyle y = -2.6$

$\displaystyle -2.6 = -5.2\cos\left(\frac{\pi}{15} (0) + \delta\right)$

$\displaystyle \frac{1}{2} = \cos\left(\delta\right)$

$\displaystyle \delta = \frac{\pi}{3}$

so ...

$\displaystyle y = -5.2\cos\left(\frac{\pi}{15} t + \frac{\pi}{3}\right)$

make sure your calculator is in radian mode when you graph it.

5. Originally Posted by captain_jonno
Hi chaps & chapettes,