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SHM · Lecture 6 of 26

All six SHM graphs: x, v and a against time and each other

By Lalit, IIT Madras

All six SHM graphs, x, v and a against time and against each other, with the phase differences between them, for JEE Main and Advanced.

Watch lecture 6

A block on a spring with a velocity arrow beside three stacked graphs against time over one period 2π/ω, showing x = A sin ωt, v = Aω sin(ωt + π/2) marked π/2 ahead of x, and a = Aω² sin(ωt + π) marked π ahead of x and π/2 ahead of v.

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What this lecture covers

Differentiating x(t) gives the v-t relation, and v(t) leads back to v(x); the a-t and a-v relations make six. A start at the mean position fixes φ, and since the sine repeats every 2 π, the period follows. Against x, acceleration is a line sloping down and velocity an ellipse. Time plots show how x, v and a differ in phase, and the a-v graph is another ellipse.

In this lecture

  1. Play from The six relations and SHM so far
  2. Play from Differentiating x(t): v-t and v-x
  3. Play from The a-t and a-v relations
  4. Play from Phi at the mean position; time period
  5. Play from The a-x graph from a = −ω² x
  6. Play from The v-x graph and why it is an ellipse
  7. Play from Graphs of x, v and a against time
  8. Play from Phase differences of x, v and a
  9. Play from The a-v graph
  10. Play from Recap: six relations, six graphs