This paper shows how to use a mathematical model to predict the vibration of lightweight timber-framed floor/ceiling systems (LTFSs) caused by mechanical excitation. The LTFS considered here is made up of an upper floor layer, a cavity space with timber joists and a ceiling. These components are joined by timber battens, ceiling furring channels and ceiling clips. The vibration in the structure is caused by a localized excitation on the top surface and the resulting vibration level of the ceiling surface will be analysed. The cavity space is filled with fibre infill for damping the sound transmitting through the cavity. A unique feature of the design and the model is the sand-sawdust mixture in the upper layer. The theoretical model and the experimental measurements show that the sand-sawdust dampens the vibration in the frequency range between 10 and 200 Hz. The damping by the sand-sawdust and the fibre infill are found by comparing the numerical simulations against the experimental measurements. We show that the simple linear frequency dependent loss factors can be used to predict the low-frequency vibrations of LTFSs.