Understanding Simple Harmonic Movement: Debunking Common Misconceptions

[zhenyazh]

Hi,
could some one please explain in detail why this things are true?

thanks

A simple pendulum suspended in a rocket ship has a period T0. Assume that the rocket ship is near the Earth in a uniform gravitational field.

True: If the ship accelerates downward at 9.81 m/s2, the pendulum will no longer oscillate.
False: If the ship accelerates upward, the period increases.
True: If the length of the pendulum is doubled, the new period will be the square root of two times T0.
False: If the mass of the pendulum is halved, the period decreases.
False: If the ship moves upward with a constant velocity, the period increases.

 

[jbsteele]

The first statement is true because when the rocket ship accelerates downward at 9.81 m/s2, the pendulum will experience a force equal to its weight and the period of oscillation will be reduced to zero. The second statement is false because acceleration is necessary in order for the period to change. The third statement is true because increasing the length of the pendulum results in an increase in its moment of inertia, so the period of oscillation increases. The fourth statement is false because changing the mass of the pendulum does not affect the period of oscillation. The fifth statement is also false because a constant velocity does not cause any change in the period of oscillation.