What factor affects the rate of exponential decay in coupled pendulums?

In summary, two pendulums, one with a large mass and the other with a small mass, are attached to the same piece of horizontal string. The large pendulum is released from an amplitude and causes the small pendulum to resonate. However, the rate of exponential decay of the large pendulum is slower than if it were a single pendulum connected to nothing else. This is due to the presence of friction, which is reduced when the pendulums are in resonance. This results in a slower rate of exponential decay.
  • #1
xlyndseyx
2
0
You have 2 pendulums attached to the same piece of horizontal string.
One pendulum has a large mass, the other is small.
They are both of the same length.
The large pendulum is released from an amplitude and so the small pendulum resonates.
The rate of exponential decay of the large pendulum is much slower, than if it were a single pendulum connected to nothing else.
How and Why is this so?
Surely the rate of exponential decay of the large pendulum should be faster and the pendulum dampened, as when energy is transferred to the small mass pendulum, some is lost from the system as it is converted to heat?

HELP!
 
Physics news on Phys.org
  • #2
The rate of exponential decay of the large pendulum is much slower, than if it were a single pendulum connected to nothing else.
From whence does this info come? Did you do an experiment?
 
  • #3
This is very interesting. Allow me to venture clarification of the setup: A 1 foot string is tacked to the end of my desk. At the end of that string I place a 1 ounce weight. At the middle of the string I place a 1/2 ounce weight.
I hold onto the 1 ounce weight and taughtly raise the string structure horizontally to the edge of my desk.
Then I let go and observe the motion of the weights as they swing down and pendulum.
Is this a fair description?
 
  • #4
Yes they're experiment results, which had me puzzled for a while!
But then i figured...FRICTION!
the pendulums which were in resonance had less friction than the single pendulum on its own, therefore the systematic error was reduced and the rate exponential decay was less.
Thanks for the replys though!
 

1. What is Simple Harmonic Motion (SHM)?

Simple Harmonic Motion is a type of periodic motion where the restoring force is directly proportional to the displacement from the equilibrium position and is always directed towards the equilibrium position. It can be described by a sine or cosine function and is frequently observed in systems such as springs, pendulums, and mass-spring systems.

2. What is resonance?

Resonance is the phenomenon that occurs when an external force is applied to a system at its natural frequency, causing it to vibrate with a larger amplitude. This can happen in various systems, such as musical instruments, where the strings or air columns vibrate at their natural frequencies in response to external forces.

3. How do pendulums work?

A pendulum is a simple device that consists of a mass attached to a string or rod, which is suspended from a fixed point. When the mass is pulled to one side and released, it will swing back and forth in a regular pattern, known as an oscillation. The motion of a pendulum can be described using SHM, with the restoring force being gravity.

4. What factors affect the period of a pendulum?

The period of a pendulum is affected by three main factors: the length of the string or rod, the mass of the pendulum bob, and the gravitational acceleration at the location of the pendulum. The longer the length of the pendulum, the longer the period will be. The heavier the pendulum bob, the longer the period will be. And the higher the gravitational acceleration, the shorter the period will be.

5. How is SHM related to energy?

In SHM, energy is constantly being converted between potential energy and kinetic energy. At the equilibrium position, the potential energy is at its maximum and the kinetic energy is at its minimum. As the system moves away from equilibrium, the potential energy decreases and the kinetic energy increases. At the turning points, the potential energy is at its minimum and the kinetic energy is at its maximum. The total energy in the system remains constant throughout the motion.

Similar threads

Replies
10
Views
950
  • Introductory Physics Homework Help
Replies
9
Views
696
Replies
8
Views
1K
Replies
1
Views
2K
  • Introductory Physics Homework Help
Replies
1
Views
2K
  • Advanced Physics Homework Help
Replies
4
Views
3K
Replies
3
Views
2K
Replies
3
Views
993
  • Advanced Physics Homework Help
Replies
4
Views
5K
Back
Top