A pendulum of length 2 m swings so that its bob’s horizontal displacement (from the…

MATHEMATICS · Multi-part · AP · Calculus AB · Contextual Applications of Differentiation · Contextual Applications of Differentiation

Problem

A pendulum of length 2 m swings so that its bob’s horizontal displacement xx (from the lowest point) satisfies x(t)=ℓsin⁡θ(t)x(t)=\ell\sin \theta(t), where ℓ=2\ell=2 m and θ(t)\theta(t) is the angular measure from the vertical in radians. At one instant the bob is 0.25 m to the right of the lowest point and moving horizontally at 0.60 m/s toward the center. (a) Find the value of θ\theta corresponding to x=0.25x=0.25 m. (b) Using the relation between xx and θ\theta, obtain a formula that connects dxdt\dfrac{dx}{dt} and dθdt\dfrac{d\theta}{dt}. (c) Compute dθdt\dfrac{d\theta}{dt}, in rad/s, at the given instant. Indicate whether θ\theta is increasing or decreasing and explain how you know.

Related theory

Browse the problem library