Answer:
Ö + θ ( (k/m) + (g/l)) = 0
Step-by-step explanation:
Use the FBD attached:
Apply Newtons 2 nd Law in tangential direction:
Sum ( Ft ) = m*a
Sum of all tangential forces is:
m*g*sin(θ) + k*l*sin(θ)*cos(θ) = - m*l*Ö
Using small angle approximations:
sin (θ) = θ
cos (θ) = 1
Ö = angular acceleration.
m*g*θ + k*l*θ = -m*l*Ö
Ö + θ ( (k/m) + (g/l)) = 0
Graph 1: Domain = [-6,6]
Graph 1: Range = {-5,-1,0}
Graph 2: Domain = (-4, infinity)
Graph 2: Range = {-4} or [-2, infinity)
Graph 3: Domain = (-infinity, infinity)
Graph 3: Range = [-5, infinity)
Graph 4: Domain = [-5.5, infinity)
Graph 4: Range = (-infinity, infinity)
So you have to simplify the expression so 6√6