Homework Help: Simple Harmonic Motion and amplitude help

1. Jan 28, 2010

ntox101

1. The problem statement, all variables and given/known data

A 0.50 kg particle executes linear harmonic motion about the point x = 0.0. At t= 1.0, it has a displacement x = 0.50m and a speed of 5.0 m/s to the right. The frequency of the motion is 2Hz. Determine (a) the spring constant, (b) the amplitude of the motion, (c) the displacement as a function of time t...blah blah blah...

The rest of the questions wants you to form equations and find displacements at other times which is a piece of cake.

2. Relevant equations

Acos(wt+ phase)
-wAsin(wt+phase)

3. The attempt at a solution

Spring constant is easy - 78.87 N/m.

Ok, when it is asking for amplitude I am little confused. Maybe someone can help clear it up. It says it executes linear harmonic motion at x = 0.0. Does this mean that there isn't a phase angle since it is initially at rest at t = 0s and x = 0? If there isn't a phase angle that makes solving for amplitude so much simpler since I can just set it to 0 and calculate the amplitude using the conditions at t = 1.0s.

Anybody?

2. Jan 28, 2010

Gear300

At x = 0m, the velocity is at a maximum (if it was at rest, it wouldn't oscillate). The frequency is f = 2Hz, which would mean the period is T = 0.5s. At t = 1.0s, it made two full oscillations, which would mean that at t = 0.0s, x = 0.50m. You can calculate the phase angle from this.

3. Jan 28, 2010

ntox101

How so? The way I learned to find phase angles is take the displacement equation x(t) and the velocity equation v(t). If you divide these 2, you are left with x(t) / v(t) = tan(wt + phase angle).

4. Jan 28, 2010

Gear300

I overlooked the amplitude...sorry about that. Since you know the mass, position, velocity, and spring constant, you can use the conservation of energy to find the amplitude.

5. Jan 28, 2010

ntox101

Hey there, I got the problem solved.

What I did actually was took v(t) / x(t) . If you write out the equations you will see that the amplitude cancels out and you are left with tangent of some number. I then used guess and check to find the the phase angle which took a while. It was a very painstaking procedure that took up a huge mess of paper.

I checked it using the conservation of energy and I got the same answer.

Thanks for the help.