(Solved): A modified pendulum setup is as shown below, where the mass is connected to the ceiling via a linea ...

A modified pendulum setup is as shown below, where the mass is connected to the ceiling via a linear spring (characterized by $$k$$ and $$l_0$$ ). Gravity's direction is indicated. (a) Define your reference frames and relevant quantities. Hint: the distance between $$O$$ and $$P$$ is no longer constant. (b) Obtain the EOM governing the particle's motion. How many degree of freedom does this system have? (c) Define your state-space variables and put the EOM into state-space representation.