The equation of motion for a pendulum whose base is accelerating horizontally with an acceleration a(t) is
Lθ + g sin θ = a(t)cosθ
Suppose that g = 9.81 m/s2, L = 1 m, and θ (0) = 0. Solve for and plot θ (f) for 0 ≤ / ≤ 10 s for the following three cases.
a. The acceleration is constant: a = 5 m/s2, and θ (0) = 0.5 rad.
b. The acceleration is constant: a = 5 m/s2, and θ (0) = 3 rad.
c. The acceleration is linear with time: a = 0.5t m/s2, and θ (0) = 3 rad.