A pendulum consisting of three masses is shown below. The middle mass M is fixed at the midpoint of a long string, the ends of which are tied to masses m each. The strings hang over two massless pulleys (located at the same height). The pulleys are a distance 21 apart and have negligible size. Assume that the mass M is constrained to move in a vertical line midway between the pulleys. Let 8 be the angle the string from mass M makes with the horizontal. Find the Equation of Motion for 8. What are the linearized equations of motion about the equilibrium? Find the frequency of small oscillations around the equilibrium.

A pendulum consisting of three masses is shown below. The middle mass M is fixed at the midpoint of a long string, the ends of which are tied to masses m each. The strings hang over two massless pulleys (located at the same height). The pulleys are a distance 21 apart and have negligible size. Assume that the mass M is constrained to move in a vertical line midway between the pulleys. Let 8 be the angle the string from mass M makes with the horizontal. Find the Equation of Motion for 8. What are the linearized equations of motion about the equilibrium? Find the frequency of small oscillations around the equilibrium.

Elements Of Electromagnetics

7th Edition

ISBN:9780190698614

Author:Sadiku, Matthew N. O.

Publisher:Sadiku, Matthew N. O.

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Concept explainers

Free Body Diagram

The system of forces acting on a body tends to either rotate it or make the body undergo motion. In general, when an external agent exerts a force on a body, the body undergoes translational motion and rotational motion. The body has six degrees of freedom under the influence of that force. Here, three degrees of freedom are from the translational motion while the other three are from the rotation motion. However, sometimes the bodies are not allowed to undergo any motion and are fixed, under such conditions the body is said to be constrained.

Question

Introduction to Classical Mechanics Please write the solution step-by-step. Thank you.

A pendulum consisting of three masses is shown below. The middle mass M is fixed at the
midpoint of a long string, the ends of which are tied to masses m each. The strings hang over
two massless pulleys (located at the same height). The pulleys are a distance 21 apart and have
negligible size. Assume that the mass M is constrained to move in a vertical line midway
between the pulleys. Let 8 be the angle the string from mass M makes with the horizontal.
Find the Equation of Motion for 8.
What are the linearized equations of motion about the equilibrium? Find the frequency of
small oscillations around the equilibrium.
M
-21-
0
קון

Branch of science that deals with the stationary and moving bodies under the influence of forces.

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