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1. Homework Statement
Ok here it goes, we all know that 2 springs in series (k1, k2) can be expressed as one spring with spring constant k using the following equation.
[itex]
k=\frac{1}{\frac{1}{k_{1}}+\frac{1}{k_{2}}}
[/itex]
The same holds for 2 dampers c1 and c2.
[itex]
c=\frac{1}{\frac{1}{c_{1}}+\frac{1}{c_{2}}}
[/itex]
But what would happen if we have the system shown in the attached file. Point X is connected to S via a spring k1 and damper c1 in parallell, and point S is conncted to W via a spring k2 and damper c2 in parallell.
My question: If I'm only interested in points X and W, can the system be simplified into a one spring and one damper system?
2. Homework Equations
Already stated
3. The Attempt at a Solution
My initial guess is that the dynamics between X and W can be expressed with one spring and one damper with contants
[itex]
k=\frac{1}{\frac{1}{k_{1}}+\frac{1}{k_{2}}}, c=\frac{1}{\frac{1}{c_{1}}+\frac{1}{c_{2}}}
[/itex]
For this perticular question the masses are irrelevant, however in my original problem X and W have masses but S is massless.
Thanks in advance
Ok here it goes, we all know that 2 springs in series (k1, k2) can be expressed as one spring with spring constant k using the following equation.
[itex]
k=\frac{1}{\frac{1}{k_{1}}+\frac{1}{k_{2}}}
[/itex]
The same holds for 2 dampers c1 and c2.
[itex]
c=\frac{1}{\frac{1}{c_{1}}+\frac{1}{c_{2}}}
[/itex]
But what would happen if we have the system shown in the attached file. Point X is connected to S via a spring k1 and damper c1 in parallell, and point S is conncted to W via a spring k2 and damper c2 in parallell.
My question: If I'm only interested in points X and W, can the system be simplified into a one spring and one damper system?
2. Homework Equations
Already stated
3. The Attempt at a Solution
My initial guess is that the dynamics between X and W can be expressed with one spring and one damper with contants
[itex]
k=\frac{1}{\frac{1}{k_{1}}+\frac{1}{k_{2}}}, c=\frac{1}{\frac{1}{c_{1}}+\frac{1}{c_{2}}}
[/itex]
For this perticular question the masses are irrelevant, however in my original problem X and W have masses but S is massless.
Thanks in advance
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