Consider the following simple pendulum of point mass m = 1 kg and length L = 10 meter. 20 L m T = IG : T -mg L sino I=mL²; (10) = mg L (1-coso) KE = 1/2 Iw²; w=& a) Using the small angle approximation, write down the equation of motion for the simple pendulum. b) Find algebraic expressions for the oscillation period and frequency of the pendulum. Find numeric expressions for the oscillation period and frequency. c) The pendulum is initially (t = 0) displaced from the vertical direction by an angle of 30 degrees, as shown in the picture. Find an algebraic expressions for t), good for all times t. Sketch your solution.

Consider the following simple pendulum of point mass m = 1 kg and length L = 10 meter. 20 L m T = IG : T -mg L sino I=mL²; (10) = mg L (1-coso) KE = 1/2 Iw²; w=& a) Using the small angle approximation, write down the equation of motion for the simple pendulum. b) Find algebraic expressions for the oscillation period and frequency of the pendulum. Find numeric expressions for the oscillation period and frequency. c) The pendulum is initially (t = 0) displaced from the vertical direction by an angle of 30 degrees, as shown in the picture. Find an algebraic expressions for t), good for all times t. Sketch your solution.