The position of a particle is given by the expression x = 4.00 cos(6.00 pi t + p

Question

The position of a particle is given by the expression x = 4.00 cos(6.00 pi t + pi), where x is in meters and t is in seconds. Determine the frequency. Determine period of the motion. Determine the amplitude of the motion. Determine the phase constant. Determine the position of the particle at t = 0.330 s. A particle moving along the x axis in simple harmonic motion starts from its equilibrium position, the origin, at t = 0 and moves to the right. The amplitude of its motion is 3.10 cm, and the frequency is 2.10 Hz. Find an expression for the position of the particle as a function of time. (Use the following as necessary: t, and pi) Determine the maximum speed of the particle. Determine the earliest time (t > 0) at which the particle has this speed Find the maximum positive acceleration of the particle. Find the earliest time (t > 0) at which the particle has this acceleration. Determine the total distance traveled between t = 0 and t = 0.71s

Explanation / Answer

Here ,

as x = A * cos(w * t + phi)

a) comparing , w = 6 pi rad/s

frequency = w/2pi

frequency = 6 * pi/2 * pi

frequency = 3 Hz

b)

Time period = 1/frequency

Time period = 1/3

Time period = 0.33 s

c)

compaing equations ,

A = 4 cm

A = 0.04 m

d)

phase constant , phi = pi

phi = 3.14 rad

e)
at t = 0.33 s

x = 4 * cos(6 * pi * 0.33 + pi)

x = 4 * cos(2.32 * pi )

x = 2.14 cm

the position of particle is 2.14 cm

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