Answer
a. To double the frequency, decrease L by a factor of 4.
b. To double the period, increase L by a factor of 4.
c. To double the angular frequency, decrease L by a factor of 4.
Work Step by Step
a. The frequency of a simple pendulum is $f=\frac{1}{2 \pi } \sqrt{\frac{g}{L}}$. To double the frequency, decrease L by a factor of 4.
b. The period of a simple pendulum is $T=2 \pi\sqrt{\frac{L}{g}}$. To double the period, increase L by a factor of 4.
c. The angular frequency of a simple pendulum is $\omega=\sqrt{\frac{g}{L}}$. To double the angular frequency, decrease L by a factor of 4.
