The physics
A bob on a string swings to and fro. For small swings, the period is the same for any swing size.
T = 2π √(L / g)
A pendulum clock ticks at each end of the swing. So one tick is half a period.
In a lift that speeds up going up, the bob feels more pull. In a bus that speeds up, the backward push adds at right angles. Under water, buoyancy takes part of the pull away.
lift: g + a bus: √(g² + a²) water: g (1 − σ/ρ)
On a planet, g = GM/R². A graph of T² against L is a straight line with slope 4π²/g.
A pendulum beats with a spring block when L/g = m/k. On a big swing, the string pulls hardest at the bottom.
Tmax = m g (3 − 2 cos θ₀)