The displacement of a particle at t = 0.300 s is given by the expression x = (5.00 m) cos(3.00t + 1/2), where?

Question

The displacement of a particle at t = 0.300 s is given by the expression x = (5.00 m) cos(3.00t + 1/2), where x is in meters and t is in seconds.
(a) Determine the frequency and period of the motion.
Hz
s
(b) Determine the amplitude of the motion.
m
(c) Determine the phase constant.
rad
(d) Determine the displacement of the particle at t = 0.300 s.
m

Answer 1

The period T is the value of t such that 3.00t = 2π, so the period T = 2π/3. The frequency is 1/T.

The amplitude is the coefficient of the cos term, since the value of the cos term ranges from +1 to -1. Amplitude can be given in two ways: 0 - peak, or peak to peak. In this case, 0 - peak is 5.00 m (the most common meaning), peak to peak - 10.00 m

The phase constant is the constant term inside the cos, = 1/2 (radians)

Plug in t = 3.00 into the expression:

x(3.00) = 5.00*cos(3.00*3.00 + 1/2) = 5.00 * cos(9.5), where 9.5 is radians.