An undamped single-degree-of-freedom system experiences the excitation F(t) = Fo (1-e) u(1) The quantity u(t) in...

 

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An undamped single-degree-of-freedom system experiences the excitation F(t) = Fo (1-e) u(1) The quantity u(t) in the above equation is the unit step function and a > 0 is a coefficient that determines how quickly the excitation reaches the steady-state value Fo. Assuming w = 50r rad/s, answer the following questions: 1. Determine the expression of the response to the excitation (3) normalized by the static response to Fo 2. Considering the result from Question 1 (a) Plot the response for a = 100 s against the unit step response for 1 [0, 107,] (b) Discuss and justify any differences and similarities between the results (c) Evaluate the values of a such that the system asymptotically oscillates within 25%, 10%, and 5% of the static response to Fo (d) Plot the excitation and response for each value of a identified in Question 2(c) An undamped single-degree-of-freedom system experiences the excitation F(t) = Fo (1-e) u(1) The quantity u(t) in the above equation is the unit step function and a > 0 is a coefficient that determines how quickly the excitation reaches the steady-state value Fo. Assuming w = 50r rad/s, answer the following questions: 1. Determine the expression of the response to the excitation (3) normalized by the static response to Fo 2. Considering the result from Question 1 (a) Plot the response for a = 100 s against the unit step response for 1 [0, 107,] (b) Discuss and justify any differences and similarities between the results (c) Evaluate the values of a such that the system asymptotically oscillates within 25%, 10%, and 5% of the static response to Fo (d) Plot the excitation and response for each value of a identified in Question 2(c)