For the simple pendulum of Figure 5.33, derive the governing equation of motion assuming

(a) that \(m\) is a point mass, and

(b) that the mass is a sphere with small but finite mass moment of inertia. Given \(l=10 \mathrm{~cm}\) and \(m=5 \mathrm{~kg}\), how significant is the effect of the mass moment of inertia if \(r=0.5 \mathrm{~cm}\) ? Derive the governing equation of motion using (i) Newton's second law, (ii) Lagrange's equation, and (iii) Hamilton's principle.

Transcribed Image Text:

m Figure 5.33: Simple pendulum.