# Homework Help: A simple harmonic motion is described by the displacement funtion

1. Sep 5, 2008

### misa_808

Equation given

u(t) =0.2 cos (wt) + 0.5 sin (wt), where w=3pi rad/s and displacement is in feet.

Describe the same motion using amplitute/phase format.
Describe the same motion using complex notation
For t =0.4 sec calculate u

How do you calculate u? and how do you describe the motion using amplitute and phase format based on the equation given?

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

2. Relevant equations

3. The attempt at a solution

2. Sep 5, 2008

### granpa

you need to show that you've made an effort to solve it yourself.

3. Sep 5, 2008

### HallsofIvy

For goodness, sake, certainly you know what "evaluate a functions" means!

4. Sep 5, 2008

### misa_808

sorry I am not use to this so I will post my attempt to solve the problem

5. Sep 5, 2008

### misa_808

I used the equation u(t) = Asin(wt+0)

I solved for displacement first u(t) = 0.5sin(3pi)(.4sec)+ 0

u (t) = 0.0328 and that is the answer for the first question but what I dont understand it that there is a cos cosine in the inital equation. So do I have to solve the cosine too inorder to get inorder to get the displacement or I am okay with this equation u (t) = Asin (wt + 0)

Last edited: Sep 5, 2008
6. Sep 5, 2008

### misa_808

If I were to describe the motion I would draw a picture of the sinusoidal wave and let the .5 and .2 graphed together showing waves and then I would say that a b sin wt is always 90degrees ahead of acos wt. But the sum of a cos wt and b sin wt produces a sinusoid of the same frequency....is this is correct