3. A 64 lb weight stretches a spring 4 ft in equilibrium. The weight is initially displaced 6 inches above equilibrium and given
a downward velocity of 6 ft/sec. Find its displacement for t > 0 if the medium resists the motion with a force equal to 3 times the speed in ft/sec (that is, the damping constant c = 3). Note that there is no external force in this case.
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Given:
initial angular speed, = 21.5 rad/s
final angular speed, = 28.0 rad/s
time, t = 3.50 s
Solution:
Angular acceleration can be defined as the time rate of change of angular velocity and is given by:
Now, putting the given values in the above formula:
Therefore, angular acceleration is: