Question

Consider a pendulum consisting of a "bob" of mass m hanging from a light (massless) string of length L. The bob is pulled to an angle θ with the vertical and released. The pendulum swings without friction and θ is small enough so that the small angle approximation is valid. Which, if any, of the statements below is/are true about this motion?

Answer 1

If the string length were changed to 4L, then the frequency will increase by a factor of 4.
If the mass of the pendulum bob were increased to 4m, then the oscillation frequency of the pendulum also will increase by a factor of 4.
If the pendulum were moved to Mars, which is smaller than Earth, the period of oscillation would not change.
If the pendulum were moved to Jupiter, which is much, much larger and more massive than Earth, then the cyclic frequency of oscillation would increase.
To determine the value of g, the acceleration due to gravity, by measuring the oscillations of the pendulum, you need to know both m, the mass of the pendulum bob, and L, the length of the pendulum.
If the initial amplitude doubles, the radial frequency will not change.
Some of the above statements are false.

Answer 2

thanks for your help!