Need help with mass-spring-damper system

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In summary, the system has a force acting on it and a damper attached to the same side of the mass as the force. The damper has a value of 4kg/s. A spring is attached to the opposite side of the mass with a value of 10kg/s. The opposite end of the spring is attached to another mass of 6kg. On the other side of this mass is a spring with a value of K of 5kg and a damper with a value of 4kg. Both the spring and the damper are tied to the wall. The first mass has a value of F = 6*10+4*4+10 = 44kg. The second mass has a value of 0. The
  • #1
formulajoe
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this all occurs on a horizontal plane.

a force is applied to a 2kg mass (m1). a damper is on the same side of the mass as the force and it is attached to a wall. its value is 4kg/s(b1). a spring is on the opposite side of the mass with a K value of 5(k1). the opposite end of the spring is attached to another mass of 6 kg(m2). on the other side of this mass is a spring with K of 10(k2) and a damper with a value of 4(b2). both the spring and the damper are tied to the wall. I am supposed to find a differential equation that relates the output to the input and find the laplace transform of it.
the y values correspond to the position of each mass.
heres what i have so far.
for the first mass:

F = m1*y1'' + b1*y1' + k1*y1 - k2*y2

second mass:
0 = m2*y2'' + b2*y2' - k2*y2 + k1*y1


where do i go from here?
 
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  • #2
okay, i got an answer that relates Y2 and F. numerator is 6s^2 +4s + 10
denominator is 12s^4 + 20s^3 + 66s^2 +60s +25.

i got the step response using MATLAB but it doesn't look quite right.
 
  • #3
I don't have time to work out the problem completely, but you should use the second equation to solve for [itex]y_1[/itex]:

[itex]y_1=\frac{1}{k_1}[-m_2\ddot{y_2}-b_2\dot{y_2}+k_2y_2][/itex],

and then differentiate twice to get [itex]\dot{y_1}[/itex] and [itex]\ddot{y_1}[/itex]. Then you can sub those into the first equation and take the Laplace transform.

If that's what you did, and you don't think your answer is correct, then check your algebra.
 
  • #4
can i get a confirmation that i analyzed the system properly? i mean as far as the beginning differential equations.
 
  • #5
did i set up the opening differential equations right?
 
  • #6
heres, what i got for an answer :

- 2/5 Y2 4th derivative, -32/5 Y2 3rd der. - 6/5 y2 2nd der and + 4 Y2 1st der.
is this right?
 

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

A mass-spring-damper system is a type of mechanical system that consists of a mass (or object), a spring, and a damper. The mass is attached to the spring, which in turn is attached to a fixed point. The damper is connected to the mass and the fixed point, providing resistance to the motion of the mass.

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

In a mass-spring-damper system, the mass is pulled down by gravity, causing the spring to stretch. As the spring stretches, it exerts a force on the mass, pulling it back up. The damper then acts to oppose the motion of the mass, dissipating energy and preventing the mass from oscillating indefinitely.

3. What are some real-world applications of mass-spring-damper systems?

Mass-spring-damper systems are commonly used in mechanical engineering and physics to model and study various systems, such as vehicle suspensions, shock absorbers, and earthquake-resistant buildings. They are also used in the design of musical instruments and sports equipment.

4. How do I solve problems involving mass-spring-damper systems?

To solve problems involving mass-spring-damper systems, you can use equations of motion, such as Newton's second law and Hooke's law, to determine the forces and accelerations acting on the system. You can also use mathematical modeling and simulation techniques to analyze and predict the behavior of the system.

5. What are some factors that affect the behavior of a mass-spring-damper system?

The behavior of a mass-spring-damper system can be affected by various factors, including the mass of the object, the stiffness of the spring, the damping coefficient of the damper, and the initial conditions of the system (i.e. the initial position and velocity of the mass). External forces, such as gravity or external vibrations, can also have an impact on the system's behavior.

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