Q3:A pendulum consists of a mass m and a massless stick of length I. The pendulum support oscillateshorizontally with a time dependent position given by x(t) = A cos(ot); (See Figure)x(1)mAt anytime, the position of the pendulum mass m is given by (X, Y) = (x(t) + / sine, - / cose)Then (a) Write the Lagrangian of the pendulum. (4 Marks)(b) Write the Euler-Lagrangian equation for 8. (3 Marks)(c) What is the equation in (b) in small-angle limit (→0)? (2 Mark)

We know that the lagrangian is given as L=T-V Where T= kinetic energy V= potential energy

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