If the tension along the string of a simple pendulum at the lowest position is 1% higher than the weight of the bob, show that the angular amplitude of the period is 0.1rad

Question

The topic is simple pendulum

Answer 1

The tension at the bottom is mg + mv²/L for the pendulum (work out the force balance!)

We can write that T_Bot = mg(1+v²/(Lg))

v²/(Lg) = .01 and v² = .01Lg

What is the height that the pendulum must be raised to achieve this velocity?

1/2 mv² = mgh = .005mLg or h = .005L

For pendulums or from geometry you know that h = L(1-cosθ) where θ is the vertical angle.

Solve this for theta --> .1 rads.