Differential equation models for damped vibrating systems are associated with quadratic matrix eigenvalue problems. The matrices in these systems are typically real and symmetric. The design and stabilisation of systems modelled by these equations require the determination of solutions to the inverse problem which are themselves real, symmetric and possibly with extra structure. In this paper we present a new method for pole assignment to a quadratic pencil by using affine sums. The method extends the work of Lancaster and Dai (1997) in which a similar problem for the generalized inverse eigenvalue problem is solved.