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 insertnamehere Aug26-05 11:56 PM

Simple Harmonic Motion

Hi, I would really like to know if my solution to the following question is correct, I would really really really appreciate it.

A hanging spring stretches by 35cm when an object of mass 450g is hung on it at rest. In this situation, we define its position as x=0. The object is pulled down an additional 18cm and released from rest to oscillate without friction. What is its position x at a time 84.4s later?
Find the distance traveled by the vibrating object.

Well, by using the equation -ky-mg=0 (at rest) I derived the equation
y=-mg/k. So i replaced y with 35 cm and m with 0.45kg in order to find k.
With k, i set the equation: x(t)= Acos(wt+c) c=phase constant w=angular frequency
and since this started at rest, there is no phase constant, and amplitude is 18cm so i made the equation
x(t)=0.18cos(5.29t)
then i replace the t with 84.4. Is this right?
And I'm having problems finding the distance traveled by the vibrating object.
Thanks a lot. And please, help!! :confused:

 mukundpa Aug27-05 12:26 AM

You want distance travelled not displacement, right?

During the given time how many complete oscillations. For each complete oscillation the distance travelled is 0.18 x 4 m.

 insertnamehere Aug27-05 10:47 AM

Thank you so much. But i have another question, how do you find the displacement?
and did i answer the question itself correctly?

 mukundpa Aug27-05 11:23 AM

The magnitude of the displacement is the distance between the final and initial position, no matter how many full oscillations are completed.

May you please explain the double posting?

 insertnamehere Aug27-05 12:34 PM