Suppose a pendulum is kept in a boat and it is oscillating. Now if the boat is made to oscillate in the same direction or opposite to that of the pendulum, how will these affect the amplitude of the bob.

Also if the boat is made to oscillate perpendicular to that of the pendulum's oscillation will the resultant oscillation of the bob be a straight line?

  • $\begingroup$ what is a bob? is it a piece of the boat? $\endgroup$
    – AoZora
    Apr 2 '19 at 9:14
  • 1
    $\begingroup$ @france95 The bob is the mass on the end of the pendulum. $\endgroup$ Apr 2 '19 at 9:29

You are solving a double pendulum: even if it is not in the standard form you have a first oscillator, the boat, to which a second oscillator, the pendulum, is attached.

Therefore you will have beats but also chaotic behaviour, see for instance this discussion https://www.math24.net/double-pendulum/ . Basically, for small oscillations, the two oscillations will become (almost) periodically in the same direction or in the opposite direction.

If you allow to he planes of the two oscillations to be different you make the system even more complicate (just google double pendulum in 3d, you should find some example).

  • 3
    $\begingroup$ This interaction between a pendulum and a boat's motion is what made absolute time keeping on ships so difficult and led to the "problem of longitude". Accurate marine chronometers, which used balance wheels instead of pendulums, did not come into general use until the early 19th century. $\endgroup$
    – gandalf61
    Apr 2 '19 at 10:35

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