Consider a bob on a light stiff rod, forming a simple pendulum of length L = 1.20 m. It is displaced from the vertical by an angle θmax and then released. Predict the subsequent angular positions if θmax is small or if it is large. Proceed as follows: Set up and carry out a numerical method to integrate the equation of motion for the simple pendulum:
Take the initial conditions to be θ = θmax and dθ/dt = 0 at t = 0. On one trial choose θmax = 5.00°, and on another trial take θmax =100°. In each case find the position θ as a function of time. Using the same values of θmax, compare your results for θ with those obtained from θ (t) = θmax cos wt. How does the period for the large value of θmax compare with that for the small value of .max? Note: Using the Euler method to solve this differential equation, you may find that the amplitude tends to increase with time. The fourth-order Runge–Kutta method would be a better choice to solve the differential equation. However, if you choose Δt small enough, the solution using Euler’s method can still be good.