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Given a pendulum of length

`L`

and a point mass

`M`

with input

`u(t)`

as the force applied tangential to the direction of the motion of the mass shown in Figure 1, Figure 1: A pendulum. a) 2 points. Write an exact input/output differential equation using

`\theta (t)`

as the output. Hint: Themoment of inertia here is

`I=ML^(2)`

. b) 2 points. Classify this system: i. Memoryless, lumped, or distributed. ii. Causal or noncausal. iii. Linear or nonlinear. c) 2 points. Write a linear approximation of the input/output differential equation from part a) assuming

`\theta (t)`

is small. d) 2 points. Find the impulse response and transfer function of the system in part c).