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Simple Harmonic Motion, Finding Time

  • Thread starter Ithryndil
  • Start date
  • #1
142
0
[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 = [tex]\sqrt{k/m}[/tex]


The Attempt at a Solution



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

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

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?
 

Answers and Replies

  • #2
Erf
2
0
Just as a quick notice, your "plug in" values have inconsistent units... you have both cm and m
Would that fix the problem?
 
  • #3
142
0
That shouldn't matter because the units for the arccos(x/A) should simply cancel each other out.
 
  • #4
alphysicist
Homework Helper
2,238
1
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 [itex]\phi[/itex] 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.
 
  • #5
142
0
Ok. Thank you for your help. That worked.
 

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