Chapter 6: Problem 5
\(\dagger\) A particle of mass \(m\) is attached by identical light elastic strings of natural length \(a\) and modulus of elasticity \(\lambda\) to four points \(A\), \(B, C\), and \(D\), which lie at the corners of a square of side \(2 a\) in a horizontal plane. In equilibrium, the particle hangs under gravity at a distance \(a \sqrt{2}\) below \(A B C D\). Show that \(m g=\lambda \sqrt{8}\). Find the normal frequencies for small oscillations about equilibrium and describe the normal modes.