Question

Problem 3-Under the ambient condiion, one can use the oscillation frequency of a spring-mass system to determine the mass suspended at the end of a spring using equation where f if the frequency of oscillation in the unit of s1, k is the spring constant in the unit of N/m, and m is the mass of the oscillating object in the unit of kg. The spring constant k is obtained by suspending an object of known mass mo under the spring and measuring its static extension L under gravity. Thus, the equation for m is a) When mo-0.1 kg, the static extension of the spring was found to be 4.7 mm. What is the value of k? Use g 9.81 m/s. What is the oscillation frequency of this test mass? b) A student suspended an object of an unknown mass under the spring and recorded eight frequencies of oscillation. They are listed below f (s7.510 7.502 7.510 7.550 7.578 7.565 7.579 7.573 PN Please compute mass m that corresponds to the eight measured frequencies. Then, compute the average, variance, and standard deviation of this measurement, and calculate 68%, 95%, and 97.7% confidence intervals of the average c) The scale used to measure mo can reach accuracy of 0.001 g. The caliper used to measure L has an accuracy of 0.1 mm·The frequency counter that measures frequency of oscillation f has an accuracy of 0.001 s.The local gravitational acceleration is known to the accuracy of 0.01 m/s. What is the error propagated into measured m? Of the above four accuracies (or inaccuracies), is there one that is clearly dominating the system error?

Answer 1