Why cant you use the laplace transform method for nonlinear

Why cant you use the laplace transform method for non-linear models? Specifically the one in the case below

Consider a pendulum consisting of a sphere of mass m suspended by a rod of negligable mass. The damping coefficient is b. There is a time dependant applied torque T(t). Initially the pendulum is at position theta_0 with angular velocity w_0. The angle theta is measured from the equillibrium position where the pendulum is hanging straight down.

Solution

The limitation of Leplace transform is that, it can\'t be used for non-linear problem. First one has to make the non-linear problem into the linear one and then use it, otherwise Laplace transform method is usually of no real use in nonlinear problems, just because one don\'t get a nice algebraic equation out of it.

If the consider the equilibrium equation of the system of rod and sphere, then after appling the torque, the ball get rotated with some angular acceleration, which is the 2nd order differential in terms of thera_0. Thus, the equation in general is of 2nd order nature, which can\'t be solved by Leplace transform.