When a forcing function F is independent of the system it acts on, then the forcing function is called ideal. Formally, the excitation may be expressed as a pure function of time. For example consider a system driven by a sinusoidal excitation F=A cos(ω_(dr)t) having frequency ω_(dr) and amplitude A. In this case, the excitation is completely independent of the system response: that is, regardless of the motion the excitation imparts on the system the system never manifests any influence on the excitation source. In contrast, a forcing function dependent on the response of the system is said to be non-ideal. If in a certain model its ideal source is replaced by a non-ideal source the excitation can be put in the form F(Φ), where Φ is a function which depends on the response of the system. Therefore, a non-ideal source cannot be expressed as a pure function of time, but rather as an equation that relates the source to the system of equations that describes the system. Hence, non-ideal systems always have one additional degree of freedom as compared with similar ideal systems.
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机译：当强制函数F与其作用的系统无关时，则将该强制函数称为理想函数。形式上，激励可以表示为时间的纯函数。例如，考虑一个由正弦激励F = A cos（ω_（dr）t）驱动的系统，它的频率为ω_（dr），振幅为A。在这种情况下，激励完全独立于系统响应：即，无论激励作用在系统上的运动系统永远不会对激励源产生任何影响。相反，依赖于系统响应的强迫函数被认为是不理想的。如果在某个模型中将其理想源替换为非理想源，则可以将激励形式设为F（Φ），其中Φ是取决于系统响应的函数。因此，非理想源不能表示为时间的纯函数，而可以表示为将源与描述系统的方程组相关的方程。因此，与类似的理想系统相比，非理想系统始终具有一个额外的自由度。
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