# Conservation of energy of a pendulum

1. Sep 4, 2011

### knowNothing23

A pendulum is suspended from the ceiling and attached to a
spring fixed to the floor directly below the pendulum support. The
mass of the pendulum bob is m, the length of the pendulum is L, and the force
constant is k. The unstressed length of the spring is L/2 and the distance between
the floor and ceiling is 1.5L. The pendulum is pulled aside so that it makes an
angle θ with the vertical and is then released from rest. Obtain an expression for
the speed of the pendulum bob as the bob passes through a point directly below
the pendulum support.

I'll set point 1, when the pendulum is about to move and point 2, when it reaches the lowest point. Then use conservation of energy. I'm not sure, where to include the potential energy of the spring. Please, help.

2. Sep 4, 2011

### PeterO

When you pull it aside [to your point 1] the spring will be stretched - some stored energy there, and the bob will be further from the floor than when at point 2 so the extra height will give some PE gain..

When the bob passes through its lowest point [your point 2] there is no energy stored in the spring, and the extra height [so PE] has also gone.
Your conservation of energy should work from there.

3. Sep 6, 2011

### knowNothing23

Thank you, Peter. Now, it's clear.