Bifurcation structures of the classical Morse oscillator with different shapes of periodic forces are studied numerically in detail. The external periodic forces considered in our study are sine wave, square wave, symmetric and asymmetric saw tooth waves, rectified sine wave and modulus of sine wave. Transcritical bifurcation, period doubling bifurcation, chaos, intermittency, periodic windows, reverse period doubling bifurcation, period-3 bubble orbit are found to occur due to the applied forces. Numerical results are demonstrated through bifurcation diagram, phase portrait and Poincare map. A comparative study of various forces is also performed.