A simple pendulum comprises of an object suspended by a string. The object is assumed to be a particle. The string, with its top end fixed, has negligible mass and does not stretch. In the absence of air resistance the system oscillates by swinging backward and forward in a vertical plane. When the string is 2.05 m long and forms an initial angle of 35.0 degrees with the vertical, compute the speed of the particle at the given positions.
(i) At the lowest point in the trajectory
(ii) If the angle is 15.0 degrees