How Do You Calculate the Spring Constant in a Coupled Pendulum System?

In summary, the conversation discusses a setup with two pendulums connected by a spring, with unknown mass and spring constant. It is mentioned that when one bob is fixed, the other has a period of 1.25 seconds. The goal is to find the period of each normal mode when both bobs are free, but the speaker is unsure how to find the spring constant using the given information. They suggest displacing the movable bob and finding the total restoring force from gravity and the spring.
  • #1
mewmew
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I am given a set up with two pendulums of unknown mass m, of length =.4 meters. They are connected together with a spring of unknown spring constant k. It says when one of the bobs if fixed in place the other has a period of 1.25 seconds. I am then asked to find the period of each normal mode when both bobs are free. I know I need to find k but don't understand how using the information given about the pendulum with a spring attached. I know the frequency of the pinned system but am not sure how to get k from that, as it isn't just equal to k/m.
 
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  • #2
Take the movable bob and displace it by some small distance dx from its equilibrium position. Now what is the total restoring force on it (from gravity + spring) ?
 

What is a coupled oscillator problem?

The coupled oscillator problem is a scientific concept that describes a system of oscillators that are connected and interact with each other. This can include physical oscillators such as pendulums or electrical oscillators such as electronic circuits.

What is the significance of studying coupled oscillator problems?

Studying coupled oscillator problems is important because it helps us understand the behavior of complex systems and how different components interact with each other. This knowledge can be applied in various fields such as physics, engineering, and biology.

How do you mathematically model a coupled oscillator problem?

To mathematically model a coupled oscillator problem, we use a set of equations known as coupled differential equations. These equations describe the motion and interaction of each oscillator in the system.

What are some real-life examples of coupled oscillator problems?

There are many real-life examples of coupled oscillator problems, such as the swinging of two pendulums attached to a common support, the synchronization of fireflies flashing in unison, and the interaction of neurons in the brain.

What are some techniques used to analyze coupled oscillator problems?

Some techniques used to analyze coupled oscillator problems include linearization, perturbation theory, and numerical simulations. These techniques help us understand and predict the behavior of the system under different conditions.

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