where and are given functions and v is vertical displacement (or deflection) of the beam and c is constant and called as the wave speed. This equation corresponds to free vibrations of simply supported beam with L length. The equation for wave speed is
where EI is flexural rigidity of the section of the beam with length L, is density and A is area of cross-section of the beam. The load is suddenly removed the beam will vibrate freely.
Obtain the expression for the free undamped transverse vibration of the simply supported beam and natural frequency expression of the beam by using the Method of Separation of Variables.
Obtain expression of free vibration for simply supported beam if P (w, Q) is removed suddenly at time t = 0.
Draw the modes of deflection along the beam and modes of deflection with time along the beam (for three different values).