Consider the motion of a pendulum that is supported by springs that are elastically restrained to horizontal motion, as depicted in Figure 5.38. Assume that the springs are massless and remain horizontal, that \(\theta\) is small, and \(r\) is a constant. Formulate the equations of motion using

(a) Newton's second law,

(b) Lagrange's equation, and

(c) Hamilton's principle. Show that the period \(\tau\) is given by

\[ \tau=2 \pi \sqrt{\frac{m g+2 k r}{2 k g}} \]

Transcribed Image Text:

k m massless wheel k 0 m Figure 5.38: Pendulum supported by horizontal springs.