Spring - Damper - Mass System (in series)

In summary, the conversation discusses setting up equations for a spring-damper-mass system in series. The equations involve two subsystems, with one describing the relationship between the mass and external force, and the other describing the relationship between the spring and damper forces. The origin of the X axis is at the fixed wall, and the lengths or positions of the spring, damper, and mass are denoted as x1 and x2. After some confusion and clarification, the equations are determined to be m d(x1-x2)/dt^2 = F - d dx2/dt and c x1 = d dx2/dt.
  • #1
LittleFill
2
0
Spring - Damper - Mass System in series

fixed-----Spring-----Damper-----Mass----->F
c d m
--> -->
x1 x2

I need help setting up the equations, I know it has to have 2 subsystems but I just can't figure out the two equations I'm supposed to get.

thanks in advance
 
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  • #2
Could it be something like:

m d(x1 + x2)/dt^2 = F - d dx2/dt

c x1 = d dx2/dtAs in:

Mass x acceleration = external force - counteracting damper force
Spring force = damper force (= reaction force on the fixed 'wall')

With the origin of the X axis at the fixed wall (duh) and its plus direction pointing to the right.

Took x1 and x2 to be the lengths of the spring and damper, respectively. ('Picture' isn't too clear.)
Just in case they're really the positions of the spring-damper midpoint and the mass, well... replace x1 + x2 with x2 and wherever it says x2 above should become x2 -x1...
 
  • #3
yea it is after stayin a while in the library and looking at a couple of books i finally figured it out.
and it was x1-x2 and x2-x1 i really should have looked at my drawing again after it was posted it was much clearer before i pressed on submit (alot of empty spaces weren't there anymore)

thank you!
 

FAQ: Spring - Damper - Mass System (in series)

What is a spring-damper-mass system in series?

A spring-damper-mass system in series is a mechanical system that consists of a mass connected to a spring and a damper in a linear fashion. The mass represents the weight of an object, the spring provides the restoring force, and the damper dissipates energy to dampen the system's oscillations.

What is the equation of motion for a spring-damper-mass system in series?

The equation of motion for a spring-damper-mass system in series is given by mx'' + cx' + kx = 0, where m is the mass, c is the damping coefficient, k is the spring constant, and x is the displacement of the mass from its equilibrium position.

How does the stiffness of the spring affect the behavior of a spring-damper-mass system in series?

The stiffness of the spring affects the frequency and amplitude of the system's oscillations. A stiffer spring (higher spring constant) will result in a higher frequency and smaller amplitude of oscillations, while a less stiff spring (lower spring constant) will result in a lower frequency and larger amplitude of oscillations.

What is the role of the damping coefficient in a spring-damper-mass system in series?

The damping coefficient determines the rate at which the energy of the system is dissipated. A higher damping coefficient will result in faster energy dissipation and shorter oscillations, while a lower damping coefficient will result in slower energy dissipation and longer oscillations.

How can a spring-damper-mass system in series be used in real-world applications?

A spring-damper-mass system in series has many practical applications, such as shock absorbers in vehicles, suspension systems in buildings, and vibration isolation systems in machinery. These systems are designed to reduce the effects of external forces or vibrations and provide a smoother and more stable motion.

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