Consider a spring-mass system where a weight is resting on a frictionless table. We let \(d(t)\) denote the distance from the wall (where the spring is attached) to the weight at time \(t\) in seconds and know that the weight oscillates periodically with a minimum value of \(2\) feet and a maximum value of \(7\) feet with a period of \(2 \pi\text{.}\) We also know that \(d(0) = 4.5\) and \(d\left(\frac{\pi}{2}\right) = 2\text{.}\)

Determine a formula for \(d(t)\) in the form \(d(t) = a\cos(t-b)+c\) or \(d(t) = a\sin(t-b)+c\text{.}\) Is it possible to find two different formulas that work? For any formula you find, identify the anchor point.