Modeling with periodic functions: Cyclical exponential decay. A spring is attached to the ceiling and pulled 14 cm down from equilibrium and released. After 2 seconds the amplitude has decreased to 5 cm. Also, the spring oscillates 7 times each second. Assuming that the amplitude is decreasing exponentially, below is a model for the distance, D the end of the spring is below equilibrium, in terms of seconds, t: D(t) = 14(0.59761)* . cos(147t) • COS [Note: Here we define t as the number of seconds elapsed. Also, locations below the resting position have negative values for D.] After t = 8 seconds, how far from equilibrium is the end of the spring? If your answer is a decimal, please round to no more than 3 decimal places. cm

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Differential Equations

Have you ever observed the movement of the satellites and rockets or how the planets go around the sun in their orbits? How will you determine their motion? Definitely they follow some scientific laws and these kinds of problems are framed as differential equations.