Subscribe

SHM · Lecture 8 of 26

Finding the SHM phase constant from where the particle starts

By Lalit, IIT Madras

Finding the SHM phase constant φ from the starting point, for JEE: two angles fit, and the direction of motion picks one.

Watch lecture 8

A chalkboard headed 'The start fixes φ' shows a reference circle with the starting point at the top marked φ = 0 and its shadow on the horizontal diameter, a spring-block below with a velocity arrow pointing right, and a table giving x = A sin ωt for a start at the mean going plus and x = −A sin ωt for a start at the mean going minus.

Watch on YouTube Length

What this lecture covers

Reading an SHM equation comes first: amplitude, ω, period and the position at t = 0. Finding φ from the start hits a snag, since two angles give the same sine, and the direction of motion decides. Four starts worth knowing are set out next. A circle method then finds φ = π/6, φ = 5 π/6 and a start with x = A sin(ω t + 5 π/4), and gives velocity and acceleration too.

In this lecture

  1. Play from The phasor circle and trigonometry
  2. Play from Reading an SHM equation
  3. Play from Finding φ from the start
  4. Play from The four starts to know
  5. Play from The circle method: direction picks φ
  6. Play from Worked example: φ = π/6
  7. Play from Worked example: φ = 5 π/6
  8. Play from Worked example: φ = 5 π/4
  9. Play from Reading v and a off the circle
  10. Play from Recap: phase constant from the start