Simple Harmonic Motion, Finding Time

[Ithryndil]

[SOLVED] Simple Harmonic Motion, Finding Time

Homework Statement

A 0.400 kg object attached to a spring with a force constant of 8.00 N/m vibrates in simple harmonic motion with an amplitude of 10.0 cm.

Calculate the time interval required for the object to move from x = 0 to x = 4.00 cm.

Homework Equations

The relevant equations for this should be:

x = Acos(ωt)

w = $$\sqrt{k/m}$$

The Attempt at a Solution

You should be able to solve the above equation for t...

cos(ωt) = x/A
ωt = arccos(x/A)
$$t = arccos(x/A)/\sqrt{k/m}$$

Plugging in the following values:

x = 4 cm
A = 10 cm
k = 8 N/m
m = 0.400 kg

I get that t = .259s which is not right. Where am I going wrong?

 

[Erf]

Just as a quick notice, your "plug in" values have inconsistent units... you have both cm and m
Would that fix the problem?

 

[Ithryndil]

That shouldn't matter because the units for the arccos(x/A) should simply cancel each other out.

 

[alphysicist]

Hi Ithryndil,

The problem is your trig function cos(w t). That function at t=0 indicates that the particle is at the positive amplitude, so you found the time to go from x=10 cm to x=4 cm.

If instead you use a sine function, since it is zero at t=0, you should be able to follow the rest of your procedure. (Or you could put a phase shift $\phi$ into your cosine function to make it act like a sine function.)

But whenever your problem depends on the oscillator being at a specific position at t=0 (and perhaps a specific velocity direction), you must make sure that your trig function has that same behavior.

 

[Ithryndil]

Ok. Thank you for your help. That worked.