Calculating Position and Distance in Simple Harmonic Motion: A Case Study

[insertnamehere]

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!

 

[mukundpa]

You want distance traveled not displacement, right?

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

 

[insertnamehere]

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

 

[mukundpa]

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]

Sorry about that

Yes, I'm sorry i didn't know that double posting was not permitted on this forum, i sincerely apologize for violating that rule as this will never happen again. And thank you very much for assisting me and pointing that out for me. Greatly appreciate it.