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SHM · Lecture 12 of 26

SHM of a vertical spring, a block on a slope, and a bullet hitting it

By Lalit, IIT Madras

Vertical spring SHM in JEE Advanced: a hanging block's mean position, a bullet that lodges in it, and masses set on or dropped onto it.

Watch lecture 12

A chalkboard titled A bullet in a block shows a wall-mounted spring k joined to a block M with a small bullet m lodged on its right and a velocity arrow v pointing left, next to the equation m × u/(M + m) = A√(k/(M + m)) and the starred boxed result A = m × u/√(k(M + m)).

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What this lecture covers

A block hanging on a spring has its mean position mg/k below the natural length, and the same period as on a table. On a slope the constant force is mg sin θ, and a block in a liquid follows the same rule. Collisions come next: a lodging bullet, solved with momentum, then a mass set gently on a moving block. The set ends with a mass that sticks to a hanging block, where the collision point is not an extreme, and one dropped from height h.

In this lecture

  1. Play from The hanging block's mean position
  2. Play from Net force and T of a hanging block
  3. Play from A block on a slope or in a liquid
  4. Play from Released from the natural length
  5. Play from A bullet that lodges in a block
  6. Play from A mass set gently on the moving block
  7. Play from A mass set gently on a hanging block
  8. Play from Strike and stick: momentum, not energy
  9. Play from A mass dropped onto a vertical spring
  10. Play from Amplitude, time to largest compression