The position of a particle is given by the expression x = 6.00 cos (2.00 pit + p

Question

The position of a particle is given by the expression x = 6.00 cos (2.00 pit + pi), where x is in meters and t is in seconds. (a) Determine the frequency. (b) Determine period of the motion. How is the period related to the frequency? (c) Determine the amplitude of the motion. The amplitude is the maximum displacement of the object from the equilibrium point. How do you find this from the equation for x(t)? (d) Determine the phase constant. What is the phase constant in the equation x(t) = cos(wt + phi)? rad (e) Determine the position of the particle at t = 0.290 s. You know the equation giving the position of the particle as a function of time. How do you use that equation to determine the position at a specific value of the time? m

Explanation / Answer

Note that

x = A cos (2 pi f t + phi)

where f = the frequency. Thus, here,

2.00 pi = 2 pi f

Thus,

f = 1 Hz [ANSWER]

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B.

As

T = 1/f,

Then

T = 1 s [ANSWER]

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C.

x = A cos (2 pi f t + phi)

As A = the amplitude above, then

A = 6.00 m [ANSWER]

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D.

x = A cos (2 pi f t + phi)

The phase constant here is phi.

Thus,

phi = pi [or, 3.1415926535...]

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E.

At t = 0.290 s, plugging in this t,

x = 6.00cos(2.00*0.290 + pi)

x = -5.0188 [ANSWER]

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