Oscillation of a pendulum subject to a horizontal trajectory with different kinds of motion

Abstract

In the children's movie The Incredibles there is a scene where Mr Incredible faces Bomb Voyage, while Incredi Boy wants to help Mr Incredible, Incredi Boy flies with Mr Incredible, who holds on to the hero's cloak, affecting Incredi Boy’s flight plan. To understand how an oscillatory movement affects non-oscillatory movement, an experimental prototype was constructed with a particle of mass m, attached to a rigid rod and without mass of length l, to a swivel of negligible mass, which was subject to a mass M. The swivel always remained on a horizontal plane, allowing the oscillatory movement of mass m. Experimental results were obtained by means of wireless sensors which recorded the spatial coordinates of the mass m. Using Lagrangian mechanics we obtained the equations of motion and expressed the possible first integrals of movement, when the movement of the mass M was: linear uniform (ULM), uniformly accelerated, (UAM), uniform circular (UCM), accelerated circular (ACM) and forced circular (FCM). The dynamics were analyzed, the equations of movement obtained, they were solved numerically, and the experimental results were compared to theoretical and numerical results.