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The Not-so-simple Pendulum 2

Things are roughened up and friction is now added to the approximate simple pendulum

Falling Beads

Age 16 to 18 Challenge Level:

Suppose that you have a large number of knitting needles and thousands of beads which can slide along needles without friction. All beads are released from rest at the same time from a point A to slide down the needles.

  • Find a shape which is formed by the beads after time $t$.
  • Describe how this shape is changing with respect to time.


Extension: In a real situation there will a friction force. The coefficient of friction is $\mu$. Suppose it is not dependent on the speed of a bead. Find the shape of beads after time $t$ and describe how it is changing.