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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!!