How to Solve a Three Mass Four Spring System for Transverse Vibration

In summary, the problem is to compute the normal modes and natural frequencies of small transverse vibrations about equilibrium in a three-mass, four-spring system with equal masses attached to a string at equal distances from one another and from the ends. The tension in the string is constant, gravity is neglected, and the string is assumed to be weightless. This is a similar system to the Two-Mass, Three-Spring System. The first step in solving this problem is to get rid of all thetas, but the method for doing so is unclear.
  • #1
mezacom
2
0

Homework Statement


Three equal masses are attached to a string at equal distances from one another and from the ends, which are rasten to supports so that there is a tension T in the string. Compute normal modes and natural frequencies of small transverse vibrations about equilibrium. Describe the normal modes.
HINT: Assume the tension constant, neglect gravity and asume the string weightless.

similar systems:
https://ccrma.stanford.edu/CCRMA/Courses/152/vibrating_systems.html

Homework Equations





The Attempt at a Solution


 
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  • #2
Welcome to PF!

Hi mezacom! Welcome to PF! :wink:

This is a Three-Mass, Four-Spring System, like the Two-Mass, Three-Spring System in your link.

Show us what you've tried, and where you're stuck, and then we'll know how to help! :smile:
 
  • #3
I know how to solve a three mass four spring system for longitudinal vibration. I have solved it and photo it and you can find it in the link.
I also photo how I think I should start my exercise with transversal vibration.
Did I start solving my problem correctly.
I don’t know how to get rid of all thetas.

http://www.mypicx.com/05272010/mass_spring_solved/
 

Related to How to Solve a Three Mass Four Spring System for Transverse Vibration

What is a mass spring system?

A mass spring system is a physical system that consists of a mass attached to a spring. The mass is free to move along a linear path, and the spring provides a restoring force that is proportional to the displacement of the mass from its equilibrium position.

What is the equation of motion for a mass spring system?

The equation of motion for a mass spring system is given by m∷ + kx = 0, where m is the mass, k is the spring constant, and x is the displacement of the mass from its equilibrium position.

How do you solve for the natural frequency of a mass spring system?

The natural frequency of a mass spring system can be calculated using the equation fn = √(k/m), where k is the spring constant and m is the mass. Alternatively, it can be determined by solving the characteristic equation m∷ + k = 0.

What is the significance of the natural frequency in a mass spring system?

The natural frequency of a mass spring system represents the frequency at which the system will oscillate when there is no external force acting on it. It is an important characteristic of the system as it determines the amplitude and period of the oscillations.

How does changing the mass or spring constant affect the behavior of a mass spring system?

Changing the mass of a mass spring system will affect its natural frequency, with a larger mass resulting in a lower natural frequency and a smaller mass resulting in a higher natural frequency. Changing the spring constant will also affect the natural frequency, with a larger spring constant resulting in a higher natural frequency and a smaller spring constant resulting in a lower natural frequency.

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