This investigation treats the vibration of a uniform beam with hinged ends which are restrained, and which has arbitrary initial conditions of motion. A representative example is discussed in which the beam is subjected to a concentrated lateral force at the mid-point of its span and released from rest at the deflected position. The equations of motion are found to be inherently nonlinear, even for small vibrations, and there is dynamic coupling of the modes. It is found that the frequencies of the various modes are functionally related to the initial conditions, particularly the amplitudes of all the modes.

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