A spring is hung vertically with one end attached to the fixed beam and the other holding a mass. That mass moves up and down and its position relative to the beam is recorded. The position function is given by s(t) = 50e-0.8tcos(2t), where t is time, measured in seconds after the mass begins to move. When 8 is negative this motion is called undamped oscillation, when 8 is positive it is referred to as damped oscillation and when 8 is 0 it’s a pure infinite oscillation. Take the fixed interval of time 0 < t < pi. What is the initial and ending position of the mass relative to the beam? What is the instantaneous velocity and acceleration of the mass at time t? What is the initial speed and in what direction is the mass moving? At what time(s) is the object showing a velocity of 0? What is happening at this(these) time(s)? What is the total displacement of the mass on the given interval of time?
A spring is hung vertically with one end attached to the fixed beam and the other holding a mass. That mass moves up and down and its position relative to the beam is recorded. The position function is given by s(t) = 50e-0.8tcos(2t), where t is time, measured in seconds after the mass begins to move. When 8 is negative this motion is called undamped oscillation, when 8 is positive it is referred to as damped oscillation and when 8 is 0 it’s a pure infinite oscillation. Take the fixed interval of time 0 < t < pi. What is the initial and ending position of the mass relative to the beam? What is the instantaneous velocity and acceleration of the mass at time t? What is the initial speed and in what direction is the mass moving? At what time(s) is the object showing a velocity of 0? What is happening at this(these)
time(s)? What is the total displacement of the mass on the given interval of time?
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