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Suppose I a holding a box in my hands, and inside the box a spring with some mass attached hangs from the cieling of the box. Initial the system is at equilibrium, then I let go of the box and it falls. If I was inside the box observing what happens, what would I see.

  1. Would the amplitude of oscillation change?

  2. Would the period change? I think so, because the effective force constant of the spring is changed because we are now in a non-inertial reference frame.

  3. The maximum speed reached by the mass, and the height above the bottom of the box at which the maximum speed is reached?

  4. The maximum height reached by the mass?

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Dropping the box is equivalent to turning off gravity, an idea called the equivalence principle.

Thus, the mass on the spring will oscillate. Its period will be unaffected. The amplitude will be however much the original equilibrium was displaced from the spring's rest length. That is, the oscillation's lowest point will be the original position of the mass. The maximum speed can be found by equating the kinetic energy of the mass when the spring is at its rest length to its potential energy when fully stretched.

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  • $\begingroup$ What if I drop it when the spring is at its lowest point in oscillation. Then the amplitude will be the same? $\endgroup$ – Joshua Benabou Jan 22 '15 at 22:37
  • $\begingroup$ Your question says the system starts at equilibrium. Are you now asking a different one? $\endgroup$ – Mark Eichenlaub Jan 22 '15 at 22:38
  • $\begingroup$ Yes, now I ask a different scenario. $\endgroup$ – Joshua Benabou Jan 22 '15 at 22:53
  • $\begingroup$ No. When you change initial conditions, the amplitude also changes. $\endgroup$ – Mark Eichenlaub Jan 22 '15 at 23:50

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