function question

**captain_jonno** · October 8th 2009, 01:37 PM

thanks skeeter

**skeeter** · October 8th 2009, 02:22 PM

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 ...

**captain_jonno** · October 8th 2009, 06:08 PM

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?

**skeeter** · October 9th 2009, 04:42 AM

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.

**HallsofIvy** · October 9th 2009, 06:00 AM

Originally Posted by captain_jonno

Hi chaps & chapettes,

What about us chapeaus?

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