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ME 6622 Final Exam Spring 2022 vv Page 2/3 The angular frequency @ = (g//)'? of small oscillations of a point pendulum of length / and mass m is measured using an optical sensor having an output £(@) = Ke (Kisa calibration constant) which can be recorded for a range of pendulum lengths /. a) For a given calibration constant K, it is desired to estimate the gravitational acceleration g from measurements of @. Based on the given information, estimate an upper bound on the measurement accuracy of E in order to assess g to within 1%. b) If E(@) is recorded (sr = 0.1V) for a range of pendulum lengths / (measured to within 0.1%) as shown in the table below, 7 (m) 1 1.5 2 2.5 3 3.5 4 45 E (Volts) 23 2.0 [1.9 1.7 1.4 1.3 1 1.0 Estimate the calibration constant K from the measurements of E and / on a least squares basis. c) Accept or reject the dependence of won / for this calibration based on a Chi-Square assessment.\ Consider the bridge circuit shown below where Ein(1) is a time harmonic signal source with variable angular frequency @, and Ri, R2, Rs, & Ra and Cy; & C2 are selected resistors and capacitors. E,() a) Determine the relations between Ri - Rs, Ci - C2, and @ for which the bridge is balanced. b) Is it possible to use the relations in part (a) to use the bridge to adjust Fia(t) to a desired frequency @ without direct measurements of its frequency? b=) Cam Scanner 
