Solve Equation of Motion for Spring Damper System

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Can you please help me solve the equation of motion for the following diagram
123.jpg


Thanks
 
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You should at least write up the equation before asking for help to solve it. So could you write the equation?
 
What I need is the equation, the rest I can work from there
 
I have not understood the figure ... The mass is attached to the spring and the dashpot?
For the system in figure (I've attached), the equation of motion is:
m\ddot{x}+c\dot{x}+kx=0
 

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Thread 'Direction Fields and Isoclines'

Thread 'Direction Fields and Isoclines'

I sketched the isoclines for $$ m=-1,0,1,2 $$. Since both $$ \frac{dy}{dx} $$ and $$ D_{y} \frac{dy}{dx} $$ are continuous on the square region R defined by $$ -4\leq x \leq 4, -4 \leq y \leq 4 $$ the existence and uniqueness theorem guarantees that if we pick a point in the interior that lies on an isocline there will be a unique differentiable function (solution) passing through that point. I understand that a solution exists but I unsure how to actually sketch it. For example, consider a...
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