Problem 3) Uncertainty and Sensor Selection Dr. James Hooke is the quality control engineer at a harmonic spring factory. He is tasked with testing the natural frequency of a simple oscillating mass-spring system: 1 k f = 2TIM where: f is the natural frequency in Hz k is the spring constant in N/m m is the mass in kg Dr. Hooke is trying to decide which set of sensors he should purchase. Sensor Option A Sensor Option B Range: 0.0 to 0.10 kg Range: 0.00 to 0.20 kg Mass Accuracy: + 2.0% Full Scale Accuracy: + 4.0% of the reading Spring Range: 0.0 to 25.0 N/m Range: 0.0 to 40.0 N/m Constant Accuracy: + 0.2 N/m Accuracy: + 0.1 N/m Assume that the average device has a mass of 0.07 kg and a spring constant is 20 N/m. Which sensor option would you recommend to Dr. Hooke? Justify your answer with appropriate calculations