Answer
The pendulum must have a length of $~~2.0~cm$
Work Step by Step
We can find an expression for $\frac{k}{m}$:
$kh = mg$
$\frac{k}{m} = \frac{g}{h}$
We can find an expression for the frequency of the block and spring:
$f = \frac{1}{2\pi}\sqrt{\frac{k}{m}}$
$f = \frac{1}{2\pi}\sqrt{\frac{g}{h}}$
We can find an expression for the frequency of the pendulum:
$f = \frac{1}{2\pi}\sqrt{\frac{g}{L}}$
We can equate the frequencies to find the required length $L$:
$f = \frac{1}{2\pi}\sqrt{\frac{g}{L}} = \frac{1}{2\pi}\sqrt{\frac{g}{h}}$
$L = h$
$L = 2.0~cm$
The pendulum must have a length of $~~2.0~cm$
