Get the ordinary differential equation of stress-strain relation for spring-dashpot system and integrate it?
Answer:
Let us formulate one mass system with one spring,and one dashpot.
Then for a linear displacement x
Disturbing force due to spring = - k x. , k= spring stiffness
Resisting force due to dash pot = - c dx/dt, c= damping factor
Gravity force due to mass (concentrated) = mg , m= mass
Differential equation of resulting harmonic motion
k x + c dx/dt = mg .
Solution of this ordinary differential equation is exponential function and available in text books of vibration .
This solution is only applicable for a single mass system .
For multimass system, things change a lot and neither one ordinary differential equation nor any integration suffice to arrive at the solution.
A matrix form of solution for the generalised displacement vector is arrived at by application of energy prinples . stress /strain is to be derived by applying proper boundary conditions from the displacement vector.
The problem requires further ellaboration.
and your back to the original so take the ssrfsd and leave it the ** alone
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