In this lab, we will observe the free response of a first order mechanical system: a rotating bicycle wheel. As shown in the figure, suppose that the bicycle wheel is suspended above the ground, and is free to rotate on its axle. Assume that the only source of damping is the axle bearing, and that after time t=0 no external torques act on the wheel. -22(1) a) Derive the differential equation describing the angu- lar velocity of the wheel (t), in terms of the moment of inertia J and the damping B. b) Assume that a time t= 0 the wheel has initial an- gular velocity fto. Solve the differential equation for response (1). c) Normally, we plot the response as (1) versus t. In- stead, suppose we plot the response as log, ((t)/no) versus t. What type of curve is this plot? If you mea- sured experimentally log, ((t)/to) as a function of t, could you determine the system time constant 7 from the curve? d) What is the time constant 7 of the system expressed in terms of the moment of inertia J and the damping B?

In this lab, we will observe the free response of a first order mechanical system: a rotating bicycle wheel. As shown in the figure, suppose that the bicycle wheel is suspended above the ground, and is free to rotate on its axle. Assume that the only source of damping is the axle bearing, and that after time t=0 no external torques act on the wheel. -22(1) a) Derive the differential equation describing the angu- lar velocity of the wheel (t), in terms of the moment of inertia J and the damping B. b) Assume that a time t= 0 the wheel has initial an- gular velocity fto. Solve the differential equation for response (1). c) Normally, we plot the response as (1) versus t. In- stead, suppose we plot the response as log, ((t)/no) versus t. What type of curve is this plot? If you mea- sured experimentally log, ((t)/to) as a function of t, could you determine the system time constant 7 from the curve? d) What is the time constant 7 of the system expressed in terms of the moment of inertia J and the damping B?

Elements Of Electromagnetics

7th Edition

ISBN:9780190698614

Author:Sadiku, Matthew N. O.

Publisher:Sadiku, Matthew N. O.

ChapterMA: Math Assessment

Section: Chapter Questions

Problem 1.1MA

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