AB1. A rigid bar, of length L and constant mass per unit length m = m/L, is pinned to a stationary frameat A. Its other end is pinned to a linear spring of stiffness k. Gravity [g] is acting in the verticaldirection. End B is horizontally displaced by a small amount and the system is left to oscillate.i. Sketch the free body diagram of the bar at some arbitrary instant.Lii. Show that the angular momentum of the bar about point A is given by H = (ml²q/3)k where qis the angle the bar makes with the vertical and qà is its time derivative (so angular velocity of the bar),and k is a unit vector perpendicular to the plane in which the bar moves. (Hint: Start by the angularmomentum of a small piece of the bar, of length dx' located at a distance of x' to point A. and thenintegrate over the whole length of the bar.ill. Drive the equation of motion governing the oscillations of the bar.iv. Calculate the frequency of vibrations.

Answered: Image /qna-images/answer/114bc258-9936-49aa-b507-1fbce83c9ee8.jpg

A 1. A rigid bar, of length L and constant mass per unit length m = m/L, is pinned to a stationary frame at A. Its other end is pinned to a linear spring of stiffness k. Gravity [g] is acting in the vertical direction, End B is horizontally displaced by a small amount and the system is left to oscillate. i. Sketch the free body diagram of the bar at some arbitrary instant. L ii. Show that the angular momentum of the bar about point A is given by H₁ = (ml²q/3)k where q is the angle the bar makes with the vertical and 4 is its time derivative (so angular velocity of the bar). and k is a unit vector perpendicular to the plane in which the bar moves. (Hint: Start by the angular momentum of a small piece of the bar, of length dx' located at a distance of x' to point A, and then integrate over the whole length of the bar. lii. Drive the equation of motion governing the oscillations of the bar. iv. Calculate the frequency of vibrations.

A 1. A rigid bar, of length L and constant mass per unit length m = m/L, is pinned to a stationary frame at A. Its other end is pinned to a linear spring of stiffness k. Gravity [g] is acting in the vertical direction, End B is horizontally displaced by a small amount and the system is left to oscillate. i. Sketch the free body diagram of the bar at some arbitrary instant. L ii. Show that the angular momentum of the bar about point A is given by H₁ = (ml²q/3)k where q is the angle the bar makes with the vertical and 4 is its time derivative (so angular velocity of the bar). and k is a unit vector perpendicular to the plane in which the bar moves. (Hint: Start by the angular momentum of a small piece of the bar, of length dx' located at a distance of x' to point A, and then integrate over the whole length of the bar. lii. Drive the equation of motion governing the oscillations of the bar. iv. Calculate the frequency of vibrations.

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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