Compound Pendulum. In class we saw the simple pendulum (point mass attached to a massless string), which is a highly idealized scenario. In this question we will explore the compound pendulum (a physical object swung around a pivot, like shown below). (a) Use torque (rotational dynamics) to show that the equation of motion is given by Ia = mgL sin 3 mine Figure 1: (left) FBD on Physical/Compound pendulum. (right) Rod pendulum where I is the moment of inertia of the object, a the angular acceleration, m the mass of the object, g the gravitational acceleration and L the distance between the pivot and center of mass of the physical pendulum. (b) Use small angle approximation to find the motion of the pendulum as (t). (c) What is the period of oscillation? (d) Suppose you have a hollow rod pendulum of mass 1 kg and of length 1 m like shown in Fig. 1 (right), also assume it is filled with 4 kg of sand. A hole suddenly appears at the bottom of the rod (t = 0) and starts to leak sand at a rate of 0.5 kg / min. Find the expression for the Period as a function of time T(t).

Compound Pendulum. In class we saw the simple pendulum (point mass attached to a massless string), which is a highly idealized scenario. In this question we will explore the compound pendulum (a physical object swung around a pivot, like shown below). (a) Use torque (rotational dynamics) to show that the equation of motion is given by Ia = mgL sin 3 mine Figure 1: (left) FBD on Physical/Compound pendulum. (right) Rod pendulum where I is the moment of inertia of the object, a the angular acceleration, m the mass of the object, g the gravitational acceleration and L the distance between the pivot and center of mass of the physical pendulum. (b) Use small angle approximation to find the motion of the pendulum as (t). (c) What is the period of oscillation? (d) Suppose you have a hollow rod pendulum of mass 1 kg and of length 1 m like shown in Fig. 1 (right), also assume it is filled with 4 kg of sand. A hole suddenly appears at the bottom of the rod (t = 0) and starts to leak sand at a rate of 0.5 kg / min. Find the expression for the Period as a function of time T(t).

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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