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SHM · Lecture 11 of 26

How to prove a motion is SHM, and k effective

By Lalit, IIT Madras

Proving a motion is SHM for JEE by reducing the net force to −kx, then reading ω, T and k effective off that force.

Watch lecture 11

A chalkboard titled k effective shows a block of mass m on a floor joined to a wall by a spring, next to the starred boxed formulas F net = −k effective x and T = 2π√(m/k effective), with notes that k effective is whatever stays with x, can be a combination of several quantities, and equals k for the block with F.

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What this lecture covers

For a horizontal spring-block the net force reduces to −kx, giving ω, the period and the frequency, with the energy method as a second route. In the SHM law F is the net force and x counts from the mean position, unlike the spring law. Under an added constant force the block still does SHM with T unchanged. Proof steps, k effective and a 0.5 kg particle in F = 8 − 2x come last.

In this lecture

  1. Play from The spring-block and its net force
  2. Play from Proving the spring-block is SHM
  3. Play from The energy method for ω
  4. Play from Spring law versus SHM law
  5. Play from Spring-block with a constant force F
  6. Play from The steps that prove a motion is SHM
  7. Play from F switched on at the natural length
  8. Play from Defining k effective; the force 8 − 2x
  9. Play from Proving the particle does SHM
  10. Play from Recap: proving SHM and k effective