# Homework Help: An object is undergoing simple harmonic motion

1. Apr 21, 2012

### Mdhiggenz

1. The problem statement, all variables and given/known data
An object is undergoing simple harmonic motion with period 1.190 and amplitude 0.640

At t=0 the object is at x=0 . How far is the object from the equilibrium position at time 0.475 ?

2. Relevant equations

3. The attempt at a solution

x=Acos(ωt+∅)

x= 0.640cos(2∏/1.190*.475)=.639

What am I doing wrong?

Thank you

- higgenz

2. Apr 21, 2012

### Curious3141

At t = 0, x = 0. What should the value of ∅ be?

You'd be better off modelling the motion as x = Asin(ωt)

3. Apr 21, 2012

### Mdhiggenz

Can you explain why you would use sin?

4. Apr 21, 2012

### Curious3141

You're told that at t = 0, x = 0. Sketch the curves of x = Asin(ωt) and x = Acos(ωt) with t representing the horizontal axis and x, the vertical. Which of them passes through the origin (0,0)?

It's OK to use the phase-shifted cosine function x = Acos(ωt + ∅) as long as you calculate the value of the phase shift ∅. But you didn't.

5. Apr 21, 2012

### Mdhiggenz

I was a bit confused on how to calculate ∅

I know the formula for ∅ is arctan(-vox/ωxo)

But isnt the initial velocity zero which would make it ∅= to 0 ?

6. Apr 21, 2012

### Curious3141

Don't get tied up in formulas you memorise. You must clearly understand the derivation of each formula you use, otherwise you'll use them in the wrong context.

Go back to what you wrote. x = Acos(ωt + ∅).

Now put t = 0 and x = 0 to get 0 = Acos(∅). So what should ∅ be?

Use this value of ∅ and try to rework your answer. You'll get a negative value, but it doesn't matter - they just want the numerical magnitude.

7. Apr 21, 2012

### Mdhiggenz

Excellent I got the answer than way as well. I appreciate you helping me out, and teaching me an alternative method!

Higgenz

8. Apr 21, 2012

### Curious3141

You're welcome.