[college differential equations] I’m not sure how to get the right answer and I’ve been stuck for a...

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[college differential equations] I’m not sure how to get the right answer and I’ve been stuck for a few hours…again

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Bd-4 is in college differential equations

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The problem in question:

A 2 pound object is suspended from a spring. The spring stretches an extra 3 inches with the weight attached. If the spring is compressed by 2 inches and released with an upward velocity of 67.8823 feet per second, find the formula describing the displacement of the object using only a single cosine function.

I found the differential equation: of .0625u” 8u=0 and the characteristic being r^{2 128=} 0 but I’m struggling to find the single cosine function version (Rcos(ωt-φ)). How would I find this? I found multiple versions of the Acos(ωt) Bsin(ωt) but I think I’ve made to many mistakes. Help?

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Bd-4

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