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SHM · Lecture 14 of 26

Springs in series and parallel in SHM: the k effective of each

By Lalit, IIT Madras

Springs in series and parallel for JEE SHM: k = k1 + k2 side by side, 1/k = 1/k1 + 1/k2 end to end, and a spring cut into pieces.

Watch lecture 14

Chalkboard titled "k and the natural length": four identical green springs joined end to end form one long spring of length nL, with the boxed formula k effective = k/n for n springs of the same material and coils.

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What this lecture covers

Side by side, springs add as k = k1 + k2. End to end they follow 1/k = 1/k1 + 1/k2, because a massless spring pulls with the same force all along. Any network then reduces to one k effective. Cutting a spring shows k is inversely proportional to its natural length, so a piece of length l/6 has 6k, and the pieces can be rejoined in parallel. Last comes an infinite set of springs in parallel, summed as an infinite GP.

In this lecture

  1. Play from Finding k effective for springs
  2. Play from Springs in parallel: k = k1 + k2
  3. Play from Springs in series: 1/k = 1/k1 + 1/k2
  4. Play from Massless spring: same pull all along
  5. Play from A network reduced to one k effective
  6. Play from Spring constant against natural length
  7. Play from A spring cut into pieces in parallel
  8. Play from An infinite set of springs in parallel
  9. Play from The sum of an infinite GP
  10. Play from Recap: series, parallel and cut springs