A mass m hangs on the end of a cord around a pulley ofradius a and moment of inertia I, as shown in Fig. 3.6.11.The rim of the pulley is attached to a spring (with constantk). Assume small oscillations so that the spring remainsessentially horizontal and neglect friction. Find the natu-ral circular frequency of the system in terms of m, a, k, 1,and g.www

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Answered: A mass m hangs on the end of a cord…

Calculus: Early Transcendentals

8th Edition

ISBN:9781285741550

Author:James Stewart

Publisher:James Stewart

Chapter1: Functions And Models

Section: Chapter Questions

Problem 1RCC: (a) What is a function? What are its domain and range? (b) What is the graph of a function? (c) How...

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Similar questions

A mass weighing 9pounds is attached to a spring whose spring constant is 36 lb/ft. What is the period of simple harmonic motion? d. a. π 2√2 b. π 4√2 C. П 3√2 π 6√3 e. π 6√2
The beam shown below is loaded with a group of parallel forces. Calculate the resultant and locate with respect to the left support and also the center of the beam. Note: There are 2 parts to this problem and each part should be worked independently (sketches, equations and calculations must be shown for each part). Part 1: Find the resultant with respect to the left support. The illustration below can be used to solve for the sum of moments about the left support. Part 2: Draw a new sketch showing the beam again with the 3 vertical forces going down. On this second sketch, the centerline of the beam should be drawn. Next, the dimensions should depict the distances from each of the 3 downward forces to the centerline of the beam.
A force of 15 Newtons stretches a spring 20 centimeters. After a 3 kilogram mass is attached to the spring, the mass is pulled down to a position √3 meters below equilibrium and released with an upward velocity of 5 meters per second. Find a. The equation of motion. b. The amplitude, period, and phase shift of the simple harmonic motion.
2. Find the length of the curve r = 4 sine from 0 = 0° to 0 = 90° and also the total length of curve. Ο Α.π;2π B. 2n ; 4n O C. 3n ; 6A O D. 4n ; 8A
a. the maximum displacement b. the frequency c. the time required for one cycle. 21. d = 5 cost 23. d = -6 cos 2πt 25. d = 1/sin 2t 2.TT 27. d = -5 sin -t 3 40° 25° 22. d = 10 cos 2πt 24. d = -8 cos 500 26. d = sin 2t Practice Plus In Exercises 29-36, find the length x to the nearest whole unit. 29. 2 3πT 28. d = -4 sin t 2

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