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

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

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

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

$
A = -5.2
$

at this point ...

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

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

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

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

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

so ...

$
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,