1. A standard pendulum of length L that swings under the influence of gravity alone (no air resistance) has a period (the time for one complete swing) in seconds of T=- du @JO V1-k sin(u) where w = g/L, k = sin(0/2), g = 9.8 m/s is the free-fall acceleration, and 0, is the initial angle from which the pendulum was released, in radians, measured from the vertical. Use the trapezoidal rule to estimate the period of a 1 metre long pendulum that is released from an angle of 0,= /4. Ensure that your estimate is correct with an error of less than 0.01 seconds. You will need to first determine how many trapezoids are needed to obtain this error bound.