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SHM · Lecture 9 of 26

Time between two positions in SHM, and when two oscillators meet

By Lalit, IIT Madras

Time between two positions in SHM, read off the reference circle as t = θ/ω, and the greatest separation of two oscillators, for JEE.

Watch lecture 9

A chalkboard headed 'From one position to another' shows a reference circle whose start and end radii enclose the angle θ, with its diameter marked −A, 0, A/2 and A above a spring-block, and a table of angles such as 0 to A/2 giving π/6, A/2 to A giving π/3 and T/6 = T/4 − T/12.

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What this lecture covers

On the reference circle, the point turns through an angle θ in time t = θ/ω, and trigonometry finds θ for any two positions. Time is not proportional to distance, so the path on the line is read first. With two particles, the points on the circle keep a fixed angle. The particles meet when their points share a vertical line, and are farthest apart when the points lie on one horizontal line.

In this lecture

  1. Play from Reference circle and the two questions
  2. Play from Time between two positions: the angle
  3. Play from Worked example with t = θ/ω
  4. Play from Time is not proportional to distance
  5. Play from Look at the path on the line first
  6. Play from Two particles on the circle
  7. Play from Two particles keep a fixed angle
  8. Play from Meeting: points share a vertical line
  9. Play from The greatest separation
  10. Play from Recap: time and two oscillators