Context: introductory mechanical vibrations, 300-level engineering. ISBN13: 978-0-13-287169-3
See problem solution below
As seen in the "Potential Energy" section, the author writes that the distance the springs compress is $$s=(a+r)\theta$$When I derive $s$ I get $\tan(\theta)=s/a$ , $s=atan(\theta)$ , and by small angle approximation $s=a\theta$. How is he getting $(a+r)$?