Question

One rope of a swing is fixed above the other rope by b. The distance between the poles of the swing is a. The lengths l1 and l2 of the ropes are such that l12+ l22 = a2 + b2 (Fig . 52)

Determine the ** T of small oscillations of the swing, neglecting the height of the swinging person in comparison with the above lengths.

Answer 1

In order to solve the problem, it is sufficient to note that the motion of the swing is a rotation about an axis passing through the points where the ropes are fixed, i.e. the system is a "tilted simple pendulum" (Fig. 190).

The component of the force of gravity mg along the rotational axis does not influence the oscillations, while the normal component mg sin a is in fact the restoring force.

Therefore, using the formula for the ** of a simple pendulum, we can write

Consequently, the ** of small oscillations of the swing is