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W/Salaam, Free vibrations are vibrations of the structure (or any other thing) that result once the structure is excited and the vibrations are let to die down without additional interference. For example if you have a pendulum at rest, you pick the bob in your hand, move it on one side and let it go. Once you let go the bob, the pendulum vibrates around the initial rest point. The period of vibration is dependent on the length of pendulum (technically the parameter that defines its stiffness) and is independent of the mass of the bob. If you measure the time the pendulum would take even as it slows down to complete a cycle, it is exactly the same. Amazing isn't it. This is an example of free vibrations. Now, forced vibrations are different. In forced vibration, you have a situation where the load producing or causing vibration of structure (or any other thing) is "continuously being applied" at a frequency. An example would be a reciporcating or centrifugal machine sitting on say concrete foundation. Operation of machine would put the foundation in vibration (machine load itself has a frequency which may or may not match with foundation natural frequency) and would force the foundation response under its frequency. The foundation will as a result vibrate based on its stiffness (like pendulum). Another example considering the case of pendulum (so that you can relate) for forced vibrations would be if you put a big fan infront of the pendulum and it vibrates under the wind of fan. Summary: In free vibrations, you disturb a structure and let it vibrate without disturbing it further. In forced vibrations, the structure is continuously being disturbed by a force applied at regular interval. That is why they are called forced vibrations as we are forcing structural response under external cyclic load. Enjoy the attached forced vibrations video as well that shows breaking of a wine glass under sound. Sound waves are what are forcing the glass to vibrate and the frequency of the sound waves has been set so that its close to natural frequency of the glass causing it to resonate and break.