Q1.
Take the bob to one side to a point P, which is at the level of the horizontal line and let it go. Observe it at the extreme points of the first couple of oscillations. Does the bob almost reach the level of the horizontal line?
Answer
Yes — on the first few swings the bob rises to almost the horizontal line on the far side, but never quite reaches it, and it falls a little further short with every swing.
| Point | Height above lowest point | Potential energy | Kinetic energy | Mechanical energy |
|---|---|---|---|---|
| P (release) | h | mgh | 0 | mgh |
| Q (lowest) | 0 | 0 | ½mv2 = mgh | mgh |
| R (far side) | h (almost) | mgh | 0 | mgh |
Why it happens: the string is inextensible and the tension in it is always perpendicular to the bob's motion, so the string does no work. Only gravity does work, and gravity simply trades potential energy for kinetic energy and back again. The sum K + U — the mechanical energy — stays at mgh, so the bob must return to the height h it started from.
Why "almost": in the real world friction at the support and air resistance do a small amount of negative work on every swing. That energy leaves as heat and sound, so the mechanical energy slowly falls, the bob rises a little less each time, and the pendulum finally stops.