Final answer:
A single degree of freedom system has one natural frequency and one corresponding natural mode shape. This frequency is known as the fundamental frequency or the natural frequency, and the system undergoes simple harmonic motion in its natural mode shape when oscillating at this frequency. Resonance occurs when an external periodic force matches this natural frequency.
Step-by-step explanation:
A single degree of freedom system has one natural frequency and one natural mode shape. The natural mode shape represents the pattern of motion that the system undergoes when it vibrates at its natural frequency. The natural frequency is the special frequency at which a system will oscillate if it is not affected by any external forces or damping; it is sometimes referred to as the fundamental frequency. As the system vibrates at this frequency, it takes on the corresponding mode shape, which for a single degree of freedom system is unique. Additional frequencies, such as overtones or harmonics, occur in systems with more degrees of freedom. It's important to note that when external forces match the natural frequency of a system, the phenomenon of resonance occurs, which can lead to large amplitude oscillations. This is due to the energy of the external forces being efficiently transferred into the oscillating system, particularly when there is little to no damping present.