Question

SHM motion and acceleration

A simple pendulum suspended in a rocket ship has a period T_o. Assume that the rocket ship is near the earth in a uniform gravitational field. Determine for each of the following statements whether it is correct or incorrect.

Correct/Incorrect If the ship moves upward with a constant velocity, the period increases.
Correct/Incorrect If the length of the pendulum is doubled, the new period will be the square root of two times.T_o.
Correct/Incorrect If the ship accelerates upward, the period increases.
Correct/Incorrect If the mass of the pendulum doubles, the period increases.
Correct/Incorrect If the ship accelerates downward at 9.81 m/s², the pendulum will no longer oscillate.

Answer 1

a)
If the ship moves upward with a constant velocity, the period increases.
Incorrect - Period is determined by g which can only change with acceleration.

b)
If the length of the pendulum is doubled, the new period will be the square root of two times.To.
Correct, as per formula.

c)
If the ship accelerates upward, the period increases.
Correct - accelerating upwards will increase g, thus decreases T.

d)
If the mass of the pendulum doubles, the period increases.
Incorrect - the mass of a pendulum as no effect on its period

e)
Correct/Incorrect If the ship accelerates downward at 9.81 m/s2, the pendulum will no longer oscillate.
Correct - if the pendulum is in free fall, there is NO restoring force