# What happends when we oscillate three pendulums next to each other?

• Idrees
In summary, when three pendulums with the same mass but different lengths are oscillated together, the first pendulum will transmit its energy to the other two. The second pendulum, with the same length as the first, will resonate and oscillate with a larger amplitude, while the third pendulum, with a slightly longer length, will oscillate with a smaller amplitude. This energy will then be transmitted back to the first pendulum and so on, resulting in a continuous transformation of energy from gravitational potential to kinetic energy and back again.
Idrees
what happends when we oscillate three pendulums next to each other??

## Homework Statement

if we have three pendula hanging from one string...and each of them separated by 5 cm, and each pendulum has same amount of mass hanging from it,, but the first two pendulums are 2.0 m long and the third one is 2.5 m long... if i set the first 2.0 m long pendulum to oscillate what will happened to the other two? please give me some hints or full answer

## Homework Equations

we don't use equations but we can think about the different heights of each pendulum

## The Attempt at a Solution

i would think once you start oscillating the first pendulum, it will moeve and strt oscillating the 2nd pendulum which are both of same height, but nothing will happened to the third pendulum, it will have no motion

you don't use equations? well the pendulum will simply start oscillating at a specific angular frequency. It won't necessarily oscillate like a simple pendulum however. There's a different moment of inertia and center of mass. Without using equations, I'd say average out the distances apart to find your center of mass. As a rule of thumb, I'd imagine that the moment of inertia of this physical pendulum would probably be similar to a point mass at that center of mass.

Thanks for youre reply,, its very useful.. but also i wanted to know what will simply happen to the motion, would one pendulum moving oscillate the second one ,, please eloborate on what will simply happpen to the motion and how will the energy be transformed when this happends? please help out

They might start out at a different oscillation periods, but a forced oscillation will quickly take over if that would happen. In which the system will resonate and oscillate all together about the center of mass.

thank you for the second reply.. and i think by energy transformation they mean what will happen to kinetic and gravitational energy.. which i can answer easily

well more correctly it's gravitational potential to kinetic energy, but you have the right idea.

I think you have a problem related to forced oscillations and resonance.
The first pendulum will "transmit" some of its energy to the other two. The one with the same length is at resonance with the first one so it will oscillate with a relatively large amplitude. The third one will oscillate with a smaller amplitude, as it's out of resonance (but not by much).
After a while the energy will be transmitted back to the first pendulum and so on.

thank you nasu heaps.. i completely understood your answer properly and thank you to godtripp aswell.. the question asked "DESCRIBE THE TRANSFORMATION OF THE ENERGY THAT OCCURS WHEN THESE PENDULAS are oscillated?? should i wirte about how the gravitational energy transforms to kinetic energy... can please help me on how to write this part aswell? thanks heaps.

## 1. What is the relationship between the oscillation of three pendulums next to each other?

The oscillation of three pendulums next to each other is known as a coupled pendulum system. This means that the motion of each pendulum affects the motion of the other pendulums in the system. The pendulums are connected through a shared support point, which allows for energy to be transferred between them.

## 2. How does the length of each pendulum affect the oscillation?

The length of each pendulum plays a crucial role in the oscillation of the system. The longer the pendulum, the slower the oscillation period, and the shorter the pendulum, the faster the oscillation period. This is because the length of the pendulum determines the distance traveled by the pendulum in one cycle, also known as the amplitude of oscillation.

## 3. What happens when one pendulum in the system is set in motion?

When one pendulum is set in motion, it transfers energy to the other pendulums through the shared support point. This leads to a phenomenon known as sympathetic vibration, where the other pendulums start oscillating at the same frequency as the first pendulum. The motion of the pendulums will continue until the energy is dissipated due to friction and air resistance.

## 4. How does the amplitude of one pendulum affect the other pendulums in the system?

The amplitude of one pendulum has a direct effect on the amplitudes of the other pendulums in the system. If the amplitude of one pendulum is increased, the amplitude of the other pendulums will also increase. This is because the energy transfer between pendulums is dependent on the amplitude of oscillation.

## 5. What factors can affect the oscillation period of the pendulums in the system?

The oscillation period of the pendulums can be affected by several factors, including the length of the pendulums, the mass of the pendulums, and the angle at which they are released. Additionally, external factors such as air resistance and friction can also affect the period of oscillation. These factors can be manipulated to create different patterns and behaviors in the coupled pendulum system.

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