A vibration sensor is depicted in Figure 1. It contains a seismic mass m= 1 gram...

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A vibration sensor is depicted in Figure 1. It contains a seismic mass m= 1 gram supported by a spring with stiffness k = 10 N/mm and a damper with damping constant c = 140 Ns/m. The sensor measures vibration of y(t) = Y sin(2t). a. [5%] Draw free body diagram of the seismic mass. b. [10% ] Derive the equation of motion. c. [10% ] If vibration of the seismic mass is x(t) = X sin(2t -a), find expression for IX/Y] d. [5%] Calculate X and a if Y = 1 mm. e. [10 %] If z = x - y, and z(t) = Z sin(2t - B). calculate Z and B. f. [10% ] If the sensor is used as an accelerometer, determine the frequency range of vibration that can be measured. WE m Figure 1 Vibration Sensor A vibration sensor is depicted in Figure 1. It contains a seismic mass m= 1 gram supported by a spring with stiffness k = 10 N/mm and a damper with damping constant c = 140 Ns/m. The sensor measures vibration of y(t) = Y sin(2t). a. [5%] Draw free body diagram of the seismic mass. b. [10% ] Derive the equation of motion. c. [10% ] If vibration of the seismic mass is x(t) = X sin(2t -a), find expression for IX/Y] d. [5%] Calculate X and a if Y = 1 mm. e. [10 %] If z = x - y, and z(t) = Z sin(2t - B). calculate Z and B. f. [10% ] If the sensor is used as an accelerometer, determine the frequency range of vibration that can be measured. WE m Figure 1 Vibration Sensor

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Here are the steps to solve this vibration sensor problem a 5 Draw free body diagram of the seismic ... View the full answer