Mass-spring-damper subsystem inside a falling block

In summary, the problem involves a mass-spring-damper subsystem falling in a container and being confined to the vertical direction. The goal is to use Lagrange's equations to find the equations of motion using generalized coordinates x1 and x2. It is mentioned that the linear spring is unstretched when x2-x1 = l. The attached picture includes relevant equations for the solution. The challenge is to set constraints for the system to only move along the y-axis and to determine the equations for the M-S-D system. The student is seeking help with understanding and solving the problem.
  • #1
nekrofred
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Homework Statement


A mass-spring-damper subsystem is falling inside a container m1. The system is confined to the vertical direction. Use Lagrange’s equations to find the EOM.

A. Use x1 and x2 as generalized coordinates.
B. The linear spring is unstretched when x2 – x1 = l.



Homework Equations



See attached picture


The Attempt at a Solution



I know the block has to be restricted to only falling along the y-axis, and not moving in the x (2-D Problem). I need to set my constraints for that. Since it is a 1 DOF Problem, and there are 2 Bodies, There should only be 1 constraint needed. But where to put it. Also, how to determine the equations with the M-S-D system.
 

Attachments

  • systemcontainer.png
    systemcontainer.png
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  • #2
I am having some trouble understanding this problem and would appreciate any help that can be given.
 

1. How does the mass-spring-damper subsystem affect the motion of a falling block?

The mass-spring-damper subsystem, also known as the harmonic oscillator, affects the motion of a falling block by providing a restoring force that opposes the force of gravity. This force causes the block to oscillate up and down as it falls, rather than simply accelerating downward.

2. What is the role of the mass in the mass-spring-damper subsystem?

The mass in the mass-spring-damper subsystem represents the physical object that is falling. It affects the system by determining the inertia of the block and how it responds to the forces of gravity and the spring and damper.

3. How does the spring constant affect the behavior of the mass-spring-damper subsystem?

The spring constant, also known as the stiffness of the spring, affects the behavior of the mass-spring-damper subsystem by determining the strength of the restoring force that the spring provides. A higher spring constant will result in a stronger restoring force and thus a higher frequency of oscillation.

4. What is the role of the damper in the mass-spring-damper subsystem?

The damper, also known as a dashpot, is responsible for dissipating energy in the system. It does this by providing a resistive force that opposes the motion of the block. This allows the system to eventually reach equilibrium and come to rest.

5. How does the initial conditions of the system affect the motion of the mass-spring-damper subsystem?

The initial conditions, such as the initial position and velocity of the block, affect the motion of the mass-spring-damper subsystem by determining the amplitude and phase of the oscillations. Different initial conditions can result in different behaviors, such as larger or smaller oscillations or a shift in the equilibrium position of the block.

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