3 . A— The restoring force that causes a pendulum to vibrate is gravity. Because things float in the Space
Shuttle rather than fall to the floor, the pendulum will not oscillate at all. However, the restoring force
that causes a spring to vibrate is the spring force itself, which does not depend on gravity. The period
of a mass on a spring also depends on mass, which is unchanged in the Space Shuttle, so the period of
vibration is unchanged as well.
4 . C— The amplitude of an object in SHM is the distance from equilibrium to the maximum
displacement. In one full period, the mass traverses this distance four times: starting from max
displacement, the mass goes down to the equilibrium position, down again to the max displacement on
the opposite side, back to the equilibrium position, and back to where it started from. This is 4
amplitudes, or 0.20 m, or 20 cm.
5 . A— The period of a pendulum isBecause L , the length of the string, is in the numerator, increasing L increases the period. Increasing g
will actually decrease the period because g is in the denominator; increasing the mass on the pendulum
has no effect because mass does not appear in the equation for period.6 . (a) The maximum speed of the mass is at the equilibrium position, where PE = 0, so all energy is
kinetic. The maximum potential energy is at the maximum displacement A , because there the mass is
at rest briefly and so has no KE. At the equilibrium position all of the PE has been converted to KE,
so
Solving for v (^) max , it is found that
Now that we have a formula for the maximum speed, we can solve the problem. Call the spot where
the speed is half-maximum position 2. Use conservation of energy to equate the energy of the
maximum displacement and position 2:
The speed v 2 is half of the maximum speed we found earlier, or Plug that in and solve
for x 2 :