Complete Question
The complete question is shown on the first uploaded image
Answer:
1 The time it would take for the bob to return back is [tex]T= 3.393\ sec[/tex]
2 small angle approximation mean that the sin of that angle which in radians  is equal to the angle i.e [tex]sin \theta = \theta[/tex]
This approximation do reach an error of 1% at about 10° hence  the small approximation is for angle less than 10°
Explanation:
From the question we are told that
  The mass of the pendulum is [tex]m_p = 8.00kg[/tex]
   The length of the cable is  [tex]L = 2.86m[/tex]
   The length of the hook from the floor is  [tex]L_h = 10m[/tex]
Generally the Time period of a pendulum is not dependent on mass
And this time period is mathematically represented as
        [tex]T = 2 \pi * \sqrt{\frac{L}{g} }[/tex]
Substituting  values
        [tex]T = 2 \pi * \sqrt{\frac{2.86}{9.8} }[/tex] Â
         [tex]= 3.393\ sec[/tex]
