FYKOS Year 30 Series 4 Problem 2 — jerky pendulum · FYKOS 30 #30.4.2
Physics · mechanics
Problem
It is well known fact that to make a train ride as comfortable as possible, when accelerating or braking, the acceleration needs to change as little as possible. It is therefore good practice when a train starts with small, constant change of acceleration. The change of acceleration is called a jerk. Determine how does the equilibrium position of a pendulum (the angle with the vertical φ). Denoting the length of the pendulum l, the train starts with a constant jerk k ( k=Δa⁄Δt, where a denotes acceleration) and the train is on Earth with acceleration due to gravity g. Bonus: Derive the equations of motion and solve them numerically for φ(0)=0 and dφ⁄dt(0)=0 for various values of k.