# Two masses which are connected each other with a spring

Homework Statement Two blocks both of mass $m$ are placed on an inclined plane making an angle $\theta$ with the ground. The two masses are connected with a spring of spring constant $k$. The coefficient of kinetic friction is $\mu _k$ for both blocks. Assume that the spring is initially stretched to a lenght $L+x_0$ where $L$ is its equilibrium lenght when it is at rest on a flat surface. Find the displacement of the two blocks ALONG THE INCLINE as a function of time,t, assuming that at that particular time the spring is still stretched. (Hint : Call the displacement of the leading block along the inclined plane $x_1$. Write the displacement of the trailing block in terms of $x_1$ and stretch in the spring, $x$. You will have two time-dependent equations in two unknowns.)

Related Equations
F=-kx (Hooke's Law), differential equations

The attempt at a solution $m\frac{d^2x_1}{dt^2}=-k(x_1+x_0)-mg\sin\theta+\mu _k mg\cos\theta$​
and general solution of this diff. equation
$x_1 = A\sin(\sqrt{k/m}t) + B\cos(\sqrt{k/m}t) - \frac{kx_0+mg\sin\theta+\mu _k mg\cos\theta}{k}$ $m\frac{d^2x_2}{dt^2}=k(x_1+x_0)-mg\sin\theta+\mu _k mg\cos\theta$​

I couldn't continue anymore. Could you help me ?

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