A ball on a spring is pulled 6 inches below its rest position and then released. After t seconds, the ball's distance, d, in inches from its rest position is given by the equation below. d=−6cosπ/3t

Question

Find all values of t for which the ball is 3 inches above its rest position. >>

Give a general formula for all the solutions by adding multiples of some positive integer n.

Answer 1

Set d = 3 = -6 cos(π/3 t), cos(π/3 t) = -1/2. Solutions are in quadrants II and III, π/3 t = 2π/3 = 2πn,π or /3 t = 4π/3 + 2πn. Multiplying by 3/π, we get t = 2 + 6n or t = 4 +6n.

I haven't figured out how to condense the series 2,4,8,10,14,16,... into a single expression.