Kinetic Energy

To solve this problem, we determine the expression for the maximum kinetic energy of a simple pendulum's bob when it oscillates with maximum angular displacement .

Step 1: Understanding Energy Conservation

The total mechanical energy is conserved and consists of potential energy (PE) and kinetic energy (KE). At maximum displacement, KE is zero and energy is purely potential.

Step 2: Calculate Maximum Potential Energy

The height above the lowest point is:

Thus, maximum potential energy is:

Step 3: Relate to Kinetic Energy

At the lowest point, all potential energy converts into kinetic energy:

Step 4: Conclusion

Therefore, the maximum kinetic energy is:

Thus, the correct answer is option (3).

Using energy conservation: .

Thus, .

For minimum vertical circle, .

Hence, ratio .

Final Answer: