This lesson covers the analysis of the transverse vibration of a beam under non-classical boundary conditions. It discusses how to obtain the frequency equation and natural frequencies of the beam. The lesson also explains how non-classical boundary conditions can occur in practical problems, such as a beam carrying a concentrated mass or resting on an elastic pad. It further elaborates on how to analyze the free transverse vibration of the beam considering damping into the equation of motion. The lesson concludes with the derivation of the expression for damp free vibration response of Euler Bernoulli beam subjected to initial conditions.

- The transverse vibration of a beam can be analyzed under non-classical boundary conditions.
- Non-classical boundary conditions can occur in practical problems like a beam carrying a concentrated mass or resting on an elastic pad.
- The frequency equation and natural frequencies of the beam can be obtained under these conditions.
- The free transverse vibration of the beam can be analyzed considering damping into the equation of motion.
- The expression for damp free vibration response of Euler Bernoulli beam can be derived subjected to initial conditions.

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