The displacement of an oscillating mass is given by x(t) = 10 cos( 3 t ). What i
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Question
The displacement of an oscillating mass is given by x(t) = 10 cos( 3 t ).What is the initial velocity of the mass at time t = 0 s?
0.0000 m/s
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Your receipt no. is 158-5797 Previous Tries
What is the initial acceleration of the mass at time t = 0 s?
m/s2
Remember that the wave equation for displacement is x(t) = Acos(?t). Find the apropriate values for the amplitude, A, and the angular velocity, ?, and substitute them, along with the given value for time (t = 0), into the equation for the acceleration a(t) = - A?2cos(?t)
Incorrect. Tries 1/2 Previous Tries
At time t = 2p s, what is the displacement of the mass?
m
Tries 0/2
At time t = 2p s, what is the velocity of the mass?
m/s
Tries 0/2
At time t = 2p s, what is the acceleration of the mass?
m/s2
Explanation / Answer
The displacement of an oscillating mass x(t) = 10 cos( 3 t )
Velocity v(t) = d x(t) / dt
= 10 x 3 [-sin3t]
= -30 sin 3t
The initial velocity of the mass at time t = 0 s is v(0) = -30 sin(0)
= 0.0000 m/s
Accleration a(t) = d v(t) / dt
= -30 x 3 cos 3t
= -90 cos 3t
The initial acceleration of the mass at time t = 0 s is a(0) = -90 cos 0
= -90 m/ s 2
(b)At time t = 2p s, the displacement of the mass x(2)= 10 cos [3 x 2]
= 10 m
At time t = 2p s,the velocity of the mass v(2) = -30 sin ( 3 x2)
= -30 x 0
= 0 m/ s
At time t = 2p s, the acceleration of the mass a(2) = -90 cos ( 3x 2)
= -90 m/ s 2
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