An object is undergoing simple harmonic motion

[Mdhiggenz]

Homework Statement

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 ?

Homework Equations

The Attempt at a Solution

x=Acos(ωt+∅)

x= 0.640cos(2∏/1.190*.475)=.639

The answer however is .379

What am I doing wrong?

Thank you

- higgenz

 

[Curious3141]

x=Acos(ωt+∅)

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

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

 

[Mdhiggenz]

Can you explain why you would use sin?

 

[Curious3141]

Can you explain why you would use sin?

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.

 

[Mdhiggenz]

I was a bit confused on how to calculate ∅

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

But isn't the initial velocity zero which would make it ∅= to 0 ?

 

[Curious3141]

I was a bit confused on how to calculate ∅

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

But isn't the initial velocity zero which would make it ∅= to 0 ?

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.

 

[Mdhiggenz]

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

Higgenz

 

[Curious3141]

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

Higgenz

You're welcome.