The equation of motion for a pendulum whose base is accelerating horizontally with an acceleration a(t) is Suppose that g = 9.81 m/s 2 , L = 1 m, and θ(˙ 0) = 0. Solve for and plot θ(t) for 0 ≤ t ≤ 10...

The equation of motion for a pendulum whose base is accelerating horizontally with an acceleration a(t) is

Suppose that g = 9.81 m/s², L = 1 m, and θ(˙ 0) = 0. Solve for and plot θ(t) for 0 ≤ t ≤ 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.