Latent force models are a Bayesian learning technique that combine physical knowledge with dimensionality reduction — sets of coupled differential equations are modelled via shared dependence on a low-dimensional latent space. Analogously, modal sound synthesis is a technique that links physical knowledge about the vibration of objects to acoustic phenomena that can be observed in data. We apply latent force modelling to sinusoidal models of audio recordings, simultaneously inferring modal synthesis parameters (stiffness and damping) and the excitation or contact force required to reproduce the behaviour of the observed vibrational modes. Exposing this latent excitation function to the user constitutes a controllable synthesis method that runs in real time and enables sound morphing through interpolation of learnt parameters.