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SHM · Lecture 2 of 26

Force, acceleration and speed through one SHM oscillation

By Lalit, IIT Madras

Force, acceleration and speed through one SHM oscillation for JEE Main and Advanced, with a = −kx/m and a max = kA/m at the extremes.

Watch lecture 2

A spring-block on a floor with arrows for displacement x, force F and acceleration a, an axis marked −A, 0 and A with speed v = 0 at the ends and v max at the middle, notes on amplitude beside it, and the boxed formulas F = −kx and a = −kx/m.

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What this lecture covers

Pulled to A and released, a block is followed through one oscillation. From A towards O the spring's pull points to the mean position, and Newton's second law gives a = −kx/m, so the block speeds up. What it does at O, where the force is zero, decides the rest of the cycle, which splits into accelerated and decelerated parts. Any force of the form −kx behaves alike. The extremes are turning points, and there the acceleration peaks at kA/m.

In this lecture

  1. Play from SHM so far, and the release point A
  2. Play from Force and a = −kx/m from A to O
  3. Play from Speed from A to O, and passing O
  4. Play from O to −A: why the block stops at −A
  5. Play from Accelerated and decelerated parts
  6. Play from Any −kx force; maximum speed at O
  7. Play from Extreme positions and amplitude
  8. Play from Maximum acceleration at the extremes
  9. Play from Recap: one full oscillation