The motion of a simple pendulum is θ = A cos(√(g/λ)t). (a) Find the string tension as a function of time, assuming θ≪1. (b) When is tension maximum, and what is its maximum value?
Select all that apply

Question

The motion of a simple pendulum is θ = A cos(√(g/λ)t). (a) Find the string tension as a function of time, assuming θ≪1. (b) When is tension maximum, and what is its maximum value?

G1 Physics · Accepted Answer

θ=A cosωt with ω=√(g/λ), so θ̇=−Aω sinωt. In the small-angle treatment used by the source, radial dynamics gives tension ≈mg+mλθ̇²=mg+mgA² sin²ωt. It is maximum when sin²ωt=1, at t=(2n+1)π/(2ω), and Tₘₐₓ=mg(1+A²). Thus all four statements are correct.