Part BCSIR NET December 2023

Lagrangian formalism and generalised coordinates

Let g denote the acceleration due to gravity and a > 0. A particle of mass m glides without friction on the cycloid $x = a (θ - sin θ), y = a (1 + cos θ), 0 \leq θ \leq 2 π$ . The equation of motion of the particle is

A. $(1 - cos θ) θ$ ̈ + ½ $sin θ (θ$ ̇ $)^{2} - (g /2 a) sin θ = 0$ ✓
B. $(1 - 2 cos θ) θ$ ̈ $+ sin θ (θ$ ̇ $)^{2} - (g / a) sin θ = 0$
C. $m (1 - 2 cos θ) θ$ ̈ $+ sin θ (θ$ ̇ $)^{2} + (g / a) sin θ = 0$
D. $m (1 - 2 cos θ) θ$ ̈ $+ (m /2) sin θ (θ$ ̇ $)^{2} - (g / a) sin θ = 0$

You have the answer. Trap Analysis is why the other three were written.

Not a worked solution repeated four times — the specific reasoning error each wrong option was built to reward.

See pricing

50 are analysed free — try those first.

The chapter behind this: Lagrangian mechanics — free to read

From Classical Mechanics › Lagrangian formalism and generalised coordinates

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