restart;

eq1 := xdot = (xk - xk1)/dt;
eq2 := xdot2 = (xk - 2*xk1 + xk2)/dt^2;
eq3 := c*xdot + k*xk + m*xdot2 = F;
sol := solve({eq1, eq2, eq3}, xk);

What am I missing here? Ty 
 

I have piecewise functon:

k := piecewise(t < t1, kmax, t1 <= t, -kmax, 2*t1 + sqrt(2)*t1 <= t, kmax, 3*t1 + 2*sqrt(2)*t1 <= t, -kmax, 4*t1 + 2*sqrt(2)*t1 <= t, 0)

Everything is a constant except time t. 

I need to Integrate it 4 times. 

sol := int(k, [t = 0 .. t, t = 0 .. t, t = 0 .. t, t = 0 .. t])

I only get result for the first two conditions from the piecewise functon (t < t1, kmax, t1 <= t, -kmax)

I need the result for complete piecewise functon. Also converting to Heaviside doesn't work. I am a complete math moron. Ty