Subscribe

SHM · Lecture 16 of 26

Simple pendulum in SHM: T = 2π√(L/g), and why it needs small angles

By Lalit, IIT Madras

The simple pendulum, T = 2 π root(L/g), and why it holds only at small angles, plus g effective in an accelerating lift, for JEE SHM.

Watch lecture 16

A pendulum bob hangs inside a box-shaped lift with mg and ma drawn downward and the tension upward, an upward acceleration arrow a beside it, and the boxed formula g effective = size of (g − a) with T = 2π√(L/g effective) on the right.

Watch on YouTube Length

What this lecture covers

The ideal pendulum's assumptions are justified first. For a displaced bob the restoring force is mg sin θ, and the small-angle approximation, θ in radians, gives T = 2 π root(L/g), as does the torque about the support. Percentage changes in T are found exactly and by the binomial approximation, valid only for small changes. An accelerating lift or vehicle swaps g for g effective. A very long pendulum, with restoring force m g x (1/L + 1/R), ends it.

In this lecture

  1. Play from The ideal simple pendulum
  2. Play from The SHM test and forces on the bob
  3. Play from Small angles give T = 2 π √(L/g)
  4. Play from Large angles, and the torque route
  5. Play from Percentage change in T: length and g
  6. Play from Binomial approximation, small changes
  7. Play from A pendulum in an accelerating lift
  8. Play from A very long pendulum
  9. Play from Restoring force m g x (1/L + 1/R)
  10. Play from An infinitely long pendulum