Asimple pendulum of mass m and length l is initially motionless at the bottom equilibrium position, θ(0) = 0. then, a constant horizontal force f0 = 1 2mg is applied to the particle. find θmax for the motion which follows.

 F₀= 12 mg   θ = 85.2º

Explanation:

When the force is applied the pendulum moves laterally, and the tension in the rope has components that reached a point balances the horizontal force. Let's apply make sure Newton

X axis

     F -Tx = 0

     F = Tx

Axis y

    Ty -W = 0

    Ty = W

Let's look for the tension components

    cos θ = Ty / T

    sin θ =Tx/T

    Ty = T cos θ

    Tx = T sin θ

Let's replace and solve the system of equations

     F = T sin θ

    mg = T cos θ

     F / mg = tan θ

    tan θ = 12 mg / mg

    θ = tan -1 12

    θ = 85.2º