Structural health monitoring systems are often limited to the use of one sensor due to cost, complexity, and weight restrictions. Therefore, there is a need to develop load and damage identification techniques that utilize only one sensor. Two passive force estimation techniques are investigated in this work. The techniques focus on either the shape or the amplitude of the magnitude of the applied force in the frequency domain. Both techniques iteratively reduce an underdetermined set of equations of motion into many overdetermined systems of equations to solve for the force estimates. The techniques are shown to locate and quantify impulsive impacts with over 97% accuracy and non-impulsive impacts with at least 87% accuracy. A filament-wound rocket motor casing is used as a test structure. Impacts not acting at a specific input degree of freedom are also accurately located depending on the distance away from the modeled input degrees of freedom, and damaging impact forces are quantified by making assumptions about the impulsive nature of the applied force.