Me soon, mass and spring equation

The user needs help with deriving the equations for a system consisting of three masses and four springs, with the mass-spring arrangement being wall-spring-mass-spring-mass-spring-mass-spring-wall. They specifically need the damped equation for this system, as they already have the equation for the undamped system. The damping function for this can take different forms, but the simplest one is linear, represented by -\nu(x_i)' where \nu is the damping coefficient. They need to incorporate this into each equation. In summary, the user needs help deriving the equations for a system consisting of three masses and four springs, with the damping function being linear and represented by -\nu(x_i)' where \
  • #1
abbaskhani
2
0
please help me soon, mass and spring equation

hi, sorry for my bad english, i need to three mass and four spring ode equations,
this system: wall -- spring -- mass -- spring -- mass -- spring -- mass -- spring -- wall

but i need this system that has damped, because i have this system equation that undamped,

undamped.jpg


please help me soon, i need damped equation soon, thanks to all :!)
 
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  • #2


People cannot read your mind! There are many possible "damping" functions, most often linear or quadratic but can have almost any form. You probably want the simplest, linear, which is of the form [itex]-\nu(x_i)'[/itex] where [itex]\nu[/itex] is the "damping coefficient". Put one of those into each equation.
 
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  • #3


thanks
 

1. What is the equation for a mass-spring system?

The equation for a mass-spring system is F = -kx, where F is the force applied to the mass, k is the spring constant, and x is the displacement of the mass from its equilibrium position.

2. How do mass and spring affect the oscillation frequency?

The mass and spring both affect the oscillation frequency of a mass-spring system. A larger mass will result in a lower frequency, while a stiffer spring (higher spring constant) will result in a higher frequency.

3. What is the relationship between spring constant and stiffness?

The spring constant and stiffness are directly proportional. A higher spring constant means a stiffer spring, and a lower spring constant means a more flexible spring.

4. How does changing the mass or spring affect the period of oscillation?

Changing the mass or spring will affect the period of oscillation. A larger mass or stiffer spring will result in a longer period, while a smaller mass or more flexible spring will result in a shorter period.

5. Can the mass-spring equation be used for any oscillating system?

No, the mass-spring equation is specifically for a mass-spring system. Other oscillating systems may have different equations, depending on the variables involved and the forces acting on the system.

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