Mass-spring-damper system "shock absorber"

In summary, the conversation discusses finding equations of motion for a mechanical system with given parameters and natural lengths of springs. The equations are derived and tested in Simulink, leading to a discussion about the equilibrium state of the system. It is concluded that the equations are correct and account for the displacement of the system.
  • #1
vaitus
2
0

Homework Statement


Find equations of motion for mechanical system given by picture, where m = 1kg, k1 = 10, k2 = 25, b = 3 and natural lengths of springs are a1 = 1m, a2 = 2m. The whole system is in a gravitational field g = 9.81m/s^2

Homework Equations

The Attempt at a Solution


I came up with
[tex] m\ddot{y} = -k_2 y + k_1 (q-y) + mg \\
b\dot{q} = -k_1(q-y)
[/tex]
but whenever I try to model it in simulink it doesn't seem right.
 

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  • #2
vaitus said:
it doesn't seem right
In what respect ?

Anyway, you can check what you get for k1=0 and for k2=0
 
  • #3
When I let k1=k2=0 the mass will just keep falling, which is ok (second picture). But when k1, k2 is what it should be then (second pic), I would guess they shouldn't have an equilibrium state at the same place.

EDIT: Oh, It should be this way because it isn't the position but it's displacement and when it doesn't have mass (the q) then it should be this.
Ok, anyway thanks
 

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Last edited:

1. What is a mass-spring-damper system shock absorber?

A mass-spring-damper system shock absorber is a type of mechanical device that is used to absorb and dissipate energy when a force is applied to it. It is commonly used in vehicles to reduce the impact of bumps and vibrations on the suspension system.

2. How does a mass-spring-damper system shock absorber work?

The shock absorber consists of a spring, a mass (usually a piston), and a fluid-filled damper. When a force is applied to the shock absorber, the spring compresses, the piston moves through the fluid, and the fluid is forced through small holes in the damper, dissipating the energy and reducing the impact on the system.

3. What factors affect the performance of a mass-spring-damper system shock absorber?

The performance of a shock absorber is affected by factors such as the stiffness of the spring, the mass of the piston, the viscosity of the fluid, and the design of the damper. Additionally, the condition and maintenance of the shock absorber can also impact its performance.

4. What are the advantages of using a mass-spring-damper system shock absorber?

The use of a shock absorber in a mass-spring-damper system provides several advantages, including improved ride comfort, increased stability and control, and reduced wear and tear on other components of the suspension system. It also helps to protect the vehicle and its occupants from excessive vibrations and impacts.

5. How can the performance of a mass-spring-damper system shock absorber be improved?

The performance of a shock absorber can be improved by adjusting the various components and parameters, such as changing the stiffness of the spring, adjusting the viscosity of the fluid, or redesigning the damper. Regular maintenance and replacement of worn or damaged parts can also help to improve the performance of the shock absorber.

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