A small lead ball of mass 2kg is suspended at the end of a light string 1m in length. A small peg, 0.5m below the suspension point, catches the string in its swing. The ball is set swinging through small angles.

A) What is the period of the pendulum?

B) The ball has started swinging on the side that does not catch the peg, at an initial height 0.05m above the low point. How high does it rise on the side where the peg restricts the pendulum length to 0.5m?

2 answers

Period now consists of two "half" periods. You know the length of both halves (T=2pi sqrt (L/g) ) Add both periods for each of the lengths, and divide by 2.

for the height, KE will be zero. Initial PE= final PE. Solve for final height from that.
Can you please detail?