# Angular Displacement Computation (Math Problem Sample)

this was a numerical analysis math question as sampled below

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

• Transform the second-order initial-value problem into a system of first-order initial-value problems.

• Compute the angular displacement

CIVL2060 Numerical Methods 2023

Student's name

Institutional affiliation

Course Nmae

Lecturer

Submission Date

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

### Other Topics:

- SPSS TESTSDescription: Exercise 10.11 Descriptives N Mean Std. Deviation Std. Error 95% Confidence Interval for Mean Minimum Maximum Lower Bound Upper Bound HIGHEST YEAR OF SCHOOL COMPLETED PROTESTANT 760 13.41 3.110 .113 13.19 13.63 0 20 CATHOLIC 3...4 pages/≈1100 words| No Sources | Other | Engineering | Math Problem |
- Physics and Natural Sciences. Engineering Math ProblemDescription: The particle moves along the positive X-axis, hence its velocity varies as V=αx, where α is a positive constant. Assuming that at the moment t=0 the particle was located at the point x=0, please find:...2 pages/≈550 words| No Sources | Other | Engineering | Math Problem |
- Five-story Building And Load Data Of ExampleDescription: Determine the total axial dead and live loads at the base of column B2 assuming that the storage occupancy is on level 4 and that all other floors...5 pages/≈1375 words| No Sources | Other | Engineering | Math Problem |