Posted by **joy** on Sunday, August 22, 2010 at 9:54am.

A pendulum is initially displaced to a height 1 y above the table

top, as in figure 1. It is released with an initial speed of 1 v = 0 . At

the lowest point of its motion, it is at a height 2 y above the

table top, and with a speed of 2 v . Derive an equation of 2 v , in

terms of 1 y and 2 y , assuming that its total mechanical energy is

conserved.

- physics -
**MathMate**, Sunday, August 22, 2010 at 6:37pm
Can you double check if figure 1 looks like this:

http://img823.imageshack.us/img823/6783/1282485265.png

If this is the case, then

equate energies, namely potential and kinetic energies:

Change in potential energy, ΔEp=mg(y2-y1)

Change in kinetic energy, ΔEk=(1/2)m(v2²-v1²)

By the law of conservation of energy, we have

ΔEp+ΔEk=0

Substitute and solve for v2, noting that v1=0.

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