Question

An object moves In simple harmonic motion described by the given equation, where t is measured in seconds and d in inches. In each exercise, graph one period of the equation. Then find the following: a. the maximum displacement, b. the frequency, c. the time required for one cycle, d. the phase shift of the motion. Describe how (a) through (d) are illustrated by your graph.

d=−2sin(πt4+π2)

Answer 1

a. The maximum displacement = 2 inches

b. Frequency, f = 0.125 Hz

c. The time required for one cycle is the period, T = 8 s

d. The phase shift θ = π/2 = 90°

Explanation:

Comparing d = -2sin(πt/4 + π/2) with d = Asin(ωt + θ).

a. The maximum displacement = 2 inches

b. Frequency, f, ωt = 2πft = πt/4 ⇒ f = 1/8 Hz = 0.125 Hz

c. The time required for one cycle is the period, T = 1/f = 1/0.125 = 8 s

d. The phase shift. Comparing θ with π/2 , the phase shift θ = π/2 = 90°

a. Is gotten from the graph as the highest value of d =2

b. It is obtained ad the inverse of the tome it takes to complete one cycle on the wave.

c. This is the time difference between successive maximum points on the wave.

d. This is obtained as the shift from the origin of the graph. The point at which the graph first cuts the time axis away from the origin is its phase shift.