Answer
$0.20$ $m$
Work Step by Step
For an simple harmonic oscillator, $E=\frac{1}{2}kA^2$.
We rearrange the formula to make $A$ its subject:
$A=\sqrt{\frac{2E}{k}}$
Then, we substitute the values to find the value of A:
$A=\sqrt{\frac{2E}{k}}=\sqrt{\frac{2(4.0J)}{200 N/m}}=0.20 m$
