Current vibration-based techniques for transformer condition monitoring mostly rely on the vibration response caused by operating excitations, which consist of electrical excitations from the core and winding. Therefore, it is worthwhile to study the electrically-excited frequency response function (FRF), as it carries information of transformer mechanical and electromagnetic properties. This paper includes a sensitivity analysis of the mechanically and electrically excited FRFs of a model transformer to the reasons behind its failures. A model power transformer is used as an example to demonstrate the variation of its vibration response to a couple of causes of transformer faults, such as looseness of clamping forces in winding and core. Experimental evidence is presented to show the quantitative description of the causes of artificial faults and to extract features of variations of FRFs that might be useful to the vibration-based detection of the causes of transformer faults in general.