The displacement of a particle at t = 0.350 s is given by the expression x = (3.00 m) cos(6.00xt), where x is in meters and 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 displacement of the particle at t = 0.350 s. m (d) At what time after t=0 does it first reach equillibrium? (e) At what time after t=0 does it reach zero velocity for the first time? (f)What total distance does it travel during the first period?

blackdivcp 2022-10-16 Answered
The displacement of a particle at t = 0.350 s is given by the expression x = (3.00 m) \cos(6.00xt), where x is in meters and 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 displacement of the particle at t = 0.350 s. m (d) At what time after t=0 does it first reach equillibrium? (e) At what time after t=0 does it reach zero velocity for the first time? (f)What total distance does it travel during the first period?
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Answers (2)

Kyle Delacruz
Answered 2022-10-17 Author has 21 answers
Expression of particle x = ( 3.00   m ) cos ( 6.00 π t ) comping with the standard equation
X = A cos ( 2 π f t + ϕ )
we have
a) 2 π f t = 600 π t
2 f = 6 f = 3 s 1   o r   f = 3 H z
Time period of motion T = 1 f
T = 1 3 = 0.333   s e c o n d
b) Amplitude of motion A=3.00 m
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Gisselle Hodges
Answered 2022-10-18 Author has 5 answers
Ans (c) at next t=0.350 s
x = ( 3.00 ) cos ( 6.00 π x ( 0.35 + 0.35 ) )
x=2.427 m
x=2.43 m
(d) For the equilibrium
x = 0 cos 6 π ( 0.35 + t ) = 0
6 π ( 0.35 + t ) = 5 π 2
t = 5 × 1 12 0.35
t=0.0666 second
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