Determine the motion expressions for each of the systems shown below by using the Euler-Lagrange equation. not skiping steps please explain i do not understand yet Pendulum of length (l) and mass (m) whose support rotates in a circle of radius (a)  in a vertical plane, with constant angular velocity ω as shown in the figure

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Free undamped vibrations

Whenever an object/system displaces in either side of its equilibrium position with the help of an external/internal means, then the object/system moves regularly or randomly on both sides of its equilibrium position. This motion is called vibration. Generally, there are three types of vibration: longitudinal vibration, transverse vibration, and torsional vibration.