Use Mathematica to obtain a numerical solution to the pendulum equation in the previous problem without approximation for the case that L = 1.000 m with the initial conditions ϕ(0) = 0.350 rad (about 20◦) and dϕ/dt = 0. Evaluate the solution for t = 0.500 s, 1.000 s, and 1.500 s. Make a graph of your solution for 0 < t < 4.00 s. Repeat your solution for ϕ(0) = 0.050 rad (about 2.9^◦) and dϕ/dt = 0. Determine the period and the frequency from your graphs. How do they compare with the solution from the previous problem?