FIGURE 3 Schematic conveyor systems where viscous damping is due to (a) the process itself or (b) a retarder to aid in stopping.

If time is measured from the instant the brake is applied so that t1=0 and if the system is brought to rest so that ω2=0, equation (3-13) simplifies to

(3-14)

Finally, after expansion of the exponential in equation (3-14) according to

and setting x=ct2/J, we see that, if c is small enough for C2 to be negligible compared to c, we then have

(3-15)

in agreement with equation (3-6), since ω1 and t2 in this equation play the role of ω0 and t in equation (3-6).