Turning $(l - \frac{m}{d} \cos(\triangle\beta + α)) \frac{m}{k} \sin(\triangle\beta + α)=\triangle\beta$ into a differential equation

Question

I have a physical system which consists of a class 2 lever, a torsion spring, a linear spring, and a point of mass. When the angle of the lever is parallel to the ground, the torsion spring is on the lever, and the linear spring is attached to it vertically. The point of the mass is attached to the other end of the linear spring. I have found a solution to the steady states of the system. I have distributed the force $F_g=mg$ to parallel and perpendicular parts to the linear spring. So I could calculate the spring force and torque $F_l=d\triangle l$ and $T_d=k\triangle\beta$. To distribute $F_g$ I need the angles $\alpha$ and $ \triangle\beta$, where $\alpha$ is the angle between the lever and ground, and $\triangle\beta$ is the angle of the torsion spring. I am mainly interested in the angle $\triangle\beta$ since everything can be calculated if I know this angle. In the picture we can see the lever's changing angle $\alpha$, the blue segment is the linear spring. The equation I have created ($l$ is the distorted length of the linear spring): $$(l - \frac{m}{d} \cos(\triangle\beta + α)) \frac{m}{k} \sin(\triangle\beta + α)=\triangle\beta$$ I was able to solve it numerically. Now comes the question: How can I describe this system with differential equations? How should I start to work it out?