The position of a particle is given by the expression x = 6.00 cos (6.00πt + π/2), where x is in meters and t is in seconds. (a) determine the frequency. 3 correct: your answer is correct. hz (b) determine period of the motion. 1/3 correct: your answer is correct. s (c) determine the amplitude of the motion. 6 correct: your answer is correct. m (d) determine the phase constant. 3.14/2 correct: your answer is correct. rad (e) determine the position of the particle at t = 0.350 s. 689 incorrect: your answer is incorrect.

Explanation:

the given equation is

x = 6 Cos (6πt + π/2)

Compare with standard equation

x = A cos (2πft + Ф)

where, A is the amplitude, f is he frequency and Ф is the phase difference.

(a) by the comparison, the frequency is

2πf = 6π

f = 3 Hz

(b) Time period is defined as the reciprocal of frequency.

T = 1/ f

T = 1/3 second = 0.33 second

(c) Amplitude, A = 6

(d) phase, Ф =  π/2 = 1.57 radian

(e) put t = 0.350 s

x = 6 cos (6 π x 0.350 +  π/2)

x = 6 cos (2.6 π)

x = - 1.854

at positions a, g kinetic energy is maximum.

at position d, potential energy is maximum.