# Particle

• Jul 10th 2006, 03:58 AM
nath_quam
Particle
$\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 AM
malaygoel
Quote:

Originally Posted by nath_quam
$\displaystyle x = 2 cos(3t+\frac{\pi}{6}\))$

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

At rest, velocity will be zero.
$\displaystyle velocity=\frac{dx}{dt}$
$\displaystyle \frac{dx}{dt}=-6sin(3t + \frac{\pi}{6})$
Since,$\displaystyle sin2\pi =0$
$\displaystyle 3t + \frac{\pi}{6}=2\pi$
$\displaystyle t=\frac{11\pi}{18}$

Keep Smiling
Malay
• Jul 10th 2006, 02:57 PM
nath_quam
Just 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 PM
dmoran
Quote:

Originally Posted by nath_quam
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

Malay's solution of 11pi/18 is approximately 1.92 so I'd say you made an error somewhere. Malay's method looks fine to me.

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 PM
nath_quam
Quote:

Originally Posted by malaygoel
At rest, velocity will be zero.
$\displaystyle velocity=\frac{dx}{dt}$
$\displaystyle \frac{dx}{dt}=-6sin(3t + \frac{\pi}{6})$
Since,$\displaystyle sin2\pi =0$
$\displaystyle 3t + \frac{\pi}{6}=2\pi$
$\displaystyle t=\frac{11\pi}{18}$

Keep Smiling
Malay

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 PM
galactus
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 PM
malaygoel
Quote:

Originally Posted by dmoran
Malay's solution of 11pi/18 is approximately 1.92 so I'd say you made an error somewhere. Malay's method looks fine to me.

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

It was a silly mistake... Sorry
I always run into problems when dealing with trigonometric values, I am more comfortable with variables.

Keep Smiling
Malay
• Jul 10th 2006, 05:57 PM
nath_quam
Thanks for your help everyone makes mistakes
• Jul 10th 2006, 05:57 PM
dmoran
Quote:

Originally Posted by malaygoel
It was a silly mistake... Sorry
I always run into problems when dealing with trigonometric values, I am more comfortable with variables.

Keep Smiling
Malay

Not a problem. Happens to all of us!

Dave
• Jul 10th 2006, 06:00 PM
malaygoel
Quote:

Originally Posted by nath_quam
Thanks for your help everyone makes mistakes

I am going to have my old signature:
"An expert is one who had made all the possible mistakes in the narrowest field"
---Niels Bohr

Keep Smiling
Malay
• Jul 11th 2006, 04:01 AM
galactus
It's easy to overlook the little things. Anyone who has done math knows that.

I do it all the time.