An object oscillates as it moves along the x-axis. Its displacement varies with time according to the equation x = 4 cos(πt + π/4) where t is in seconds What is the frequency of this motion?

This is equivalent to the fraction 1/2

Explanation:

The template for cosine is

y = A*cos(B(x-C)) + D

The B determines the period T

T = 2pi/B

In this case, B = pi,

T = 2pi/B

T = 2pi/pi

T = 2

The period is 2 seconds, which is the length of each cycle.

The frequency is 1 over the period

frequency = 1/(period)

F = 1/T

F = 1/2

F = 0.5

The frequency is 0.5 hertz to indicate that it completes 0.5 a cycle in 1 second. In other words, the speed of the object (so to speak) is 0.5 cycles per second.