Question

The following figure represents a disk of mass $m$ connected to a spring and a box of mass $m$ via a massless string. The Lagrange's equation of motion is, (a) $\ddot{\theta} - \left(\frac{g}{b}\right) + \left(\frac{k}{m}\right)\theta = 0$ (b) $\ddot{\theta} - \frac{3}{2}\left(\frac{g}{b}\right) + \frac{3}{2}\left(\frac{k}{m}\right)\theta = 0$ (c) $\ddot{\theta} + \left(\frac{g}{b}\right) + \left(\frac{k}{m}\right)\theta = 0$ (d) $\ddot{\theta} - \frac{2}{3}\left(\frac{g}{b}\right) + \frac{2}{3}\left(\frac{k}{m}\right)\theta = 0$

          The following figure represents a disk of mass $m$ connected to a spring and a box of mass $m$ via a massless string.
The Lagrange's equation of motion is,
(a) $\ddot{\theta} - \left(\frac{g}{b}\right) + \left(\frac{k}{m}\right)\theta = 0$
(b) $\ddot{\theta} - \frac{3}{2}\left(\frac{g}{b}\right) + \frac{3}{2}\left(\frac{k}{m}\right)\theta = 0$
(c) $\ddot{\theta} + \left(\frac{g}{b}\right) + \left(\frac{k}{m}\right)\theta = 0$
(d) $\ddot{\theta} - \frac{2}{3}\left(\frac{g}{b}\right) + \frac{2}{3}\left(\frac{k}{m}\right)\theta = 0$

The following figure represents a disk of mass m connected to a spring and a box of mass m via a massless string.
The Lagrange's equation of motion is,
(a) θ̈ - ((g)/(b)) + ((k)/(m))θ = 0
(b) θ̈ - (3)/(2)((g)/(b)) + (3)/(2)((k)/(m))θ = 0
(c) θ̈ + ((g)/(b)) + ((k)/(m))θ = 0
(d) θ̈ - (2)/(3)((g)/(b)) + (2)/(3)((k)/(m))θ = 0

Added by Marta M.

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