## College Physics (4th Edition)

We can rank the pendulums in order of their frequency of small-amplitude oscillations, from greatest to smallest: $c \gt a = b \gt d = e$
We can write an expression for the frequency of a pendulum: $f = \frac{\omega}{2\pi}$ $f = \frac{1}{2\pi}~\sqrt{\frac{g}{L}}$ The frequency does not depend on the mass of the bob, so changing the mass of the bob does not affect the frequency. From the equation, we can see that a longer pendulum length $L$ results in a smaller frequency. We can rank the pendulums in order of their frequency of small-amplitude oscillations, from greatest to smallest: $c \gt a = b \gt d = e$