The point of suspension of a simple pendulum is given by a harmonic motion x0 = Xo sin wt along a horizontalline, as shown in Figure.
Write the differential equation of motion for a small amplitude of oscillation using the coordinates shown.
Determine the solution for x/xo, and show that when ω=(√2ωn )the node is found at the midpoint of I.
Show that in general the distance h from the mass to the node is given by the relation
h=l(ωn/ω)2,Where ωn=(√g/l).
