Angular Displacement Computation (Math Problem Sample)

CIVL2060 Numerical Methods 2023
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Assignment 6 (5%) – Due Week 13 (Friday, 2 June 2023 at 11:59 pm)
Problem 1 (15+35 marks)
A simple pendulum is idealized by considering a bob mass swinging on an inextensible, massless rod (negligible mass relative to the bob) about a frictionless pivot (Figure 1).
Figure 1 Simple pendulum
The pendulum oscillation is described by the initial-value problem consisting of the equation of motion with initial conditions:
θ'' + g/Lsin(θ) = 0, θ(t_0) = θ_0, θ'(t_0) = ω_0
Here, L is the length of the pendulum, g acceleration due to gravity, θ the angle the pendulum makes with the vertical, θ_0 the initial angular displacement, and ω_0 the initial angular velocity.
* Transform the second-order initial-value problem into a system of first-order initial-value problems.
Solution