Question

Find the locations of the object when its velocity is one-third of the maximum speed. Treat the equilibrium position as zero, positions to the right as positive, and positions to the left as negative.

Answer 1

let x = A sin ω t describes location of object at time t

V = A ω cos ω t velocity of object at time t

Vmax = A ω max speed occurs when ω t = 0 velocity / max velocity

V / Vmax = 1/3 = cos ω t

θ = ω t angle being considered

cos θ = 1/3

1/3 max speed occurs at cos θ = ±1/3

θ = ±70.5 deg