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.

Question

Physics

Kale Briggs

20 July, 21:51

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.

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Answers (1)

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Helena Sexton · Answer 1

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