In this paper we present the results of an experimental sensitivity analysis on a vertical electrically-heated Rijke tube. We examine the shift in linear decay rates and frequencies of thermoacoustic oscillations, with and without control devices. To measure the decay rate we wait for the system to reach a steady state and then excite it with an acoustic pulse from a loudspeaker. We identify the range of amplitudes over which the amplitude decays exponentially with time. In this range, the rate of change of the amplitude is linearly proportional to the amplitude, and we calculate the constant of proportionality, the linear decay rate, which can be compared with model predictions. The aim of this work is (i) to improve the experimental techniques implemented by Rigas et al. (J. Fluid Mech., 2016, vol. 787, R1), Jamieson et al. (Int. J. Spray and Comb. Dyn., Accepted, 2016 ), using a technique inspired by Mejia et al. (Comb. and Flame, 169:287-296, 2016), and (ii) to provide experimental data for future comparison with adjoint-based sensitivity analysis. Our experimental set up is automated and we can obtain thousands of decay rates in 1/12 the time of our previous method.