Question

why the amplitude of simple pendulum is kept small?

Answer 1

to make the calculus easi...er

the proper DE is \( \large \ddot \theta +{\frac {g}{\ell }} \color{red}{\sin \theta } =0\) which is a non linear DE

for small \(\theta\), \(\sin \theta \approx \theta\) so the DE can be made linear:

\( \large \ddot \theta +{\frac {g}{\ell }} \theta =0\)

a **linear** restorative force is the hall mark of simple harmonic motion so it squares that circle too :)