$\displaystyle

x = 2 cos(3t+\frac{\pi}{6}\))

$

When does the particle first come to rest after t=0

Thanks Nath

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- Jul 10th 2006, 03:58 AMnath_quamParticle
$\displaystyle

x = 2 cos(3t+\frac{\pi}{6}\))

$

When does the particle first come to rest after t=0

Thanks Nath - Jul 10th 2006, 05:45 AMmalaygoelQuote:

Originally Posted by**nath_quam**

$\displaystyle velocity=\frac{dx}{dt}$

$\displaystyle \frac{dx}{dt}=-6sin(3t + \frac{\pi}{6})$

Since,$\displaystyle sin2\pi =0$

$\displaystyle 3t + \frac{\pi}{6}=2\pi$

$\displaystyle t=\frac{11\pi}{18}$

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Malay - Jul 10th 2006, 02:57 PMnath_quamJust Quickly
Could someone please check the above as when i graphed the velocity graph i got the first point at approx 0.95 could someone show me how to prove this exact?

Thanks Nath - Jul 10th 2006, 03:12 PMdmoranQuote:

Originally Posted by**nath_quam**

Edit: Now that I look at it, I wonder if Malay should've set it equal to pi since that's the next time it equals 0.

Dave - Jul 10th 2006, 03:28 PMnath_quamQuote:

Originally Posted by**malaygoel**

By using $\displaystyle sin2\pi =0$

doesn't that find the second point

can't we use $\displaystyle sin\pi = 0$

and finish with $\displaystyle t=\frac{5\pi}{18}$

Thanks Nath - Jul 10th 2006, 04:07 PMgalactus
You're correct Nath, it

*first*comes to rest(assuming it's moving along the positive x-axis) at $\displaystyle t=\frac{5{\pi}}{18}$

Left of the y-axis, it first comes to rest at $\displaystyle t=\frac{-\pi}{18}$

Add or subtract multiples of $\displaystyle \frac{\pi}{3}$ to arrive at any subsequent extrema. The corresponding y values are -2 or 2. - Jul 10th 2006, 05:55 PMmalaygoelQuote:

Originally Posted by**dmoran**

I always run into problems when dealing with trigonometric values, I am more comfortable with variables.

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Malay - Jul 10th 2006, 05:57 PMnath_quam
Thanks for your help everyone makes mistakes

- Jul 10th 2006, 05:57 PMdmoranQuote:

Originally Posted by**malaygoel**

Dave - Jul 10th 2006, 06:00 PMmalaygoelQuote:

Originally Posted by**nath_quam**

"An expert is one who had made all the possible mistakes in the narrowest field"

---Niels Bohr

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Malay - Jul 11th 2006, 04:01 AMgalactus
It's easy to overlook the little things. Anyone who has done math knows that.

I do it all the time.