Please help. This problem involves vibrations. Thank you. Q2. An inverted pendulum consisting of a uniform bar of mass m has a torsional spring of torsionalstiffness k at the pivot, with rest angle equal to 0 (no torque when the pendulum is vertical). Thereis no damping. Figure below.a) As in HW8, show that the equations of motion for the pendulum is:mL?mgLsin 0 – k0.3b) By using the small-angle approximation sin 0 z 0, convert the above equation into the form:að + b0 = 0. Determine a and b in terms of mass, length, gravity, stiffness, etc. This is called'linearization' (the original equation from part-a is nonlinear because sin(e) is nonlinear). Moregenerally, one uses Taylor series for linearization if about any other 0 value.c) Determine the natural frequency wn of the system. Also, for what value of stiffness k is thenatural frequency 0? For what values of stiffness k is the natural frequency real-valued? (It turnsout that the equilibrium becomes unstable when the natural frequency of this system becomescomplex valued).Here's a fun video related to this Q2 problem (a bri-cycle):https://www.youtube.com/watch?v=rNQdSfg|DNMd) Should you increase or decrease the torsional stiffness so that the torsional stiffness, so that thenatural frequency is very high.

here,we use newtons method to derived motion equation.for solution refer below images.

Q2. An inverted pendulum consisting of a uniform bar of mass m has a torsional spring of torsional stiffness k at the pivot, with rest angle equal to 0 (no torque when the pendulum is vertical). There is no damping. Figure below.

Q2. An inverted pendulum consisting of a uniform bar of mass m has a torsional spring of torsional stiffness k at the pivot, with rest angle equal to 0 (no torque when the pendulum is vertical). There is no damping. Figure below.

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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