The motion of a frictionless Foucault pendulum is described by the system of two equations x" - 2w sin(a) y + kx = 0, y" + 2wcos (a)x' + ky = 0, where a is the latitude of the place where the pendulum is located, w = 7.29 x 10-5 sec- is the angular velocity of the Earth, k = g/l with g = 9.8 m/sec and I is the length of the pendulum. Assume that the pendulum at the initial time to = 0 is at rest in the position (1, 0). Then the system must be given the following initial conditions: x(0) = 1, y(0) = 0, x'(0) = 0, y'(0) = 0. (1) Use MATLAB to compute .x = x(t) and y =y(t) for t ranging between 0 and 300 seconds and a = /4. (2) Sketch x vs t and y vs t.