Resonance occurs when the natural frequency of the system matches with the vibrating frequency. It may cause structural instabilities. To avoid this, engineers maximize the first natural frequency of the system. In many applications, the natural frequency is pre-designed. Structural engineers aim to reduce the weight of structures subject to functional and safety constraints. This motivates us to modify the frequency optimization problem to weight minimization problem, for a specified fundamental natural frequency. In this paper, we solve for weight minimization using topology optimization subject to lower bound constraint on fundamental frequency. © 2021, Springer Nature Singapore Pte Ltd.