List of top Physics Questions on Lagrangian Mechanics asked in CPET

A particle is constrained to move on a parabola \(y = kx^{2}\). The number of degrees of freedom is:

The Lagrangian of a system is given by \(L = \tfrac{1}{2}\dot{q}^{2} + q\dot{q} - \tfrac{1}{2}q^{2}\). It describes the motion of:

A particle of mass \(m\) moves under a potential \(V(x)\). The Lagrangian of the system is given by \(L = \tfrac{1}{2}m\dot{x}^2 - V(x)\). According to Lagrange's equation of motion, which of the following is the correct equation of motion for the particle?

A coordinate \(q_i\) is called cyclic (or ignorable) if: