The application of the Laplace transform to the general problem of the beam is discussed. The method requires no knowledge of normal modes often employed in the classical solution. A solution in closed form is given for the forced vibration of a hinged beam excited by a concentrated harmonic force. The result converges to the correct static curve for zero frequency. The method is extended to the problem of finding the natural frequencies of beams with concentrated mass and spring. The analysis for beams with several masses and springs is outlined.