6)  A pendulum of length 41  cm is released at a point 5 cm from its equilibrium position.  At the equilibrium position it strikes a massive solid, elastic object and bounces back almost to its release position before falling again back to its equilibrium position.  The pendulum keeps bouncing back and forth until it has struck the equilibrium position 8 times.  How long is it between release and the 8th strike?  Pendulum period equation:  T = .2 sqrt(L).

L is the length of the pendulum, so L = 41cm.  The pendulum hits the solid, elastic object 8 times, so the number of hits is 8.  A full cycle is more than one hit, but how much more is it?  One cycle is equal to the pendulum going from the drop point to the other side and back.  One hit goes from the drop point to the middle point and almost back to the drop point.  One hit is equal to 1/4 of a full cycle, so (the number of hits *2 -1)/4 equals the number of cycles.  To find the time of one cycle use the equation T = .2 sqrt(L).  To find the total time multiply the time per cycle by the number of cycles.

# of cycles = (8 * 2 - 1) / 4 = 15/4 cycles

T = .2 sqrt(41) = 1.29 s/cycle

total time = 15/4 cycles * 1.29 s/cycle = 4.84 s