# Supplying energy to pendulum

1. Mar 30, 2009

### starcrossed

I had earlier posted a question in this section, but it got moved to homework section. so i did some homework and am posting the question for some more help.

I am interested in determining the force required to be supplied to a pendulum to overcome its damping force, so that the pendulum can be kept moving.

These are the steps i followed.

1. Determing the potential energy of the pendulum.

The mass of pendulum is m=10 kg. the length of the pendulum is L=0.30 m. i am raising the pendulum by angle A=20 degrees and releasing it. The potential energy of the pendulum at 20 degrees angle of swing is

E=mgh= mgl(1-cosA)=10*9.81*0.30(1-cos(20))= 1.7733 joules.

2. i release this pendulum and it comes to rest in 50 oscillations. this total energy loss in 50 oscillations is energy loss due to friction and air resistance forces combined to gether. i will call it damping energy loss.

3. if i assume linear loss of energy the damping loss of energy per oscillation is 1.7733/50 = 0.036 joules.

4. however this is wrong assumption as the energy loss is exponential with highest energy loss in the 1st oscillation and the least energy loss in the last oscillation.

5. To calculate the max energy loss due to damping: I start the oscillation at 20 degrees angle of swing. after the first oscillation the angle of swing decrease to say 19 degrees. the potential energy of the pendulm at begining with 20 degrees angle of swing is 1.7733 joules.
E=mgh= mgl(1-cosA)

After the 1st oscillation when the pendulum returns to the same position the angle is 19 degrees. the pe at 19 degrees is 1.60. E=mgh= mgl(1-cosA)

hence the loss energy due to damping is 0.17 joules.

so if i have to keep the pendulum in motion, i should supply 0.1 joules of energy to the system.

QUESTION:

now this energy is to be supplied to the pendulum by kicking or pulling the pendulum in its direction of motion. This is the max energy that has to be supplied to pendulum to keep it moving at the same amplitude and frequency with which it started the oscillation.

now for eg we pull this pendulum with a motor, where a small string is tied with the shaft of the motor and this motor pulls the pendulum from the bottom.

my question is that what should be the torque and speed of this motor? how do i determing what force i have to apply and at what speed so that the required energy of 0.1 joules is supplied to the system?

i mean if i am using a motor to pull this swing...at what speed this pendulum be pulled? should the motor be rotated in such a way that it pulls the pendulum at twice the speed of its oscillation or 1.2 times the speed of its oscillation..? how do i determing this ?