Equivalent stiffness and damping

[Hood]

Homework Statement

A scheme of springs and dampers is given. What is equivalent stiffness and damping?

Homework Equations

For stiffness in series: k_eq=k_a*k_b/(k_a+k_b)
For stiffness in parallel: k_eq=k_a+k_b
For dampers similarly.

The Attempt at a Solution

To me it looks like k₁ and k₂ are in parallel. After summation I'd say that k₃ is in series and calculate for that. Dampers c₁ and c₂ seem to be in series so I'd calculate them similarly.

I'm puzzled because textbook says that k₃ is parallel to k₁ and k₂ and simply sums it up (k_eq=k₁+k₂+k₃). I doubt it's like that, could you also explain about c₁ and c₂?

 

[rude man]

Homework Statement

A scheme of springs and dampers is given. What is equivalent stiffness and damping?

Homework Equations

For stiffness in series: k_eq=k_a*k_b/(k_a+k_b)
For stiffness in parallel: k_eq=k_a+k_b
For dampers similarly.

The Attempt at a Solution

To me it looks like k₁ and k₂ are in parallel. After summation I'd say that k₃ is in series and calculate for that. Dampers c₁ and c₂ seem to be in series so I'd calculate them similarly.

I'm puzzled because textbook says that k₃ is parallel to k₁ and k₂ and simply sums it up (k_eq=k₁+k₂+k₃). I doubt it's like that, could you also explain about c₁ and c₂?

Best thing to do is go back to Newton: mx'' = ƩF_x.

Call x = 0 when the mass is in its equilibrium position. If m goes up (x > 0) what are the forces acting on m?

You will see that your textbook is right ...