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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3.) Imagine a string that is fixed at both ends (for example, a guitar string). When plucked, the string forms a standing wave. The displacement, u(x, t), of the string varies with position x and time t. Suppose a,t) = 2sin(xx)sin() for 0 0. At a fixed point in time, the string forms a wave on 10, 11. Alternatively, if you focus on a point on the string (fix a value of r), that point oscillates up and down in time. a.) What is the period of the motion in time? За.) du 3b.) dt b.) Find the rate of change of the displacement with respect to time at a constant position (which is the vertical velocity of a point on the string.) 3c.) x = c.) At a fixed time, what point on the string is moving fastest? 3d.) t = d.) At a fixed position on the string, when is the string moving fastest? du 3e.) e.) Find the rate of change of displacement with respect to position at a constant time (which is the slope of the string.) 3f.) r =, f.) At a fixed time, where is the slope of the string the greatest?
Suppose that we have a mass-spring system that follows the simple harmonic motion described by the equation s= 6cos(pi t) , where s represents displacement measured in centimeters and time is measured in seconds. The maximum displacement of the mass is ___cm. The system's frequency is ____cycles per second. The displacement of the mass after 3/2 second is____ The first time where the mass passes through the equilibrium point is _____ .
A frog is sitting on the edge of a playground carousel with radius 1 meter. The ray through the frog's position and the center of the carousel makes an angle of measure e with the horizontal, and his starting coordinates are approximately (0.81, 0.59). Find his new coordinates after the carousel rotates by each of the following amounts. a. 2 z*+ y* = 1 C. d. (0.81,0.59) 2 е. - f. 2 g. T- 20 h. -20 b.
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.
QUESTIONS 2.1. A force of P defined by the angle 0x 75° to the horizontal acts through a point. What are the components of this force on the x- and y-axes? [See Figure 2.59(Q1).] Answer: P = 0.26P, Py = 0.97P. =
When a car hits a certain bump on the road, a shock absorber on the car is compressed a distance of 5 in., then released. The shock absorber vibrates in damped harmonic motion with a frequency of 3 cycles per second. The damping constant for this particular shock absorber is 2.5.How long does it take for the amplitude of the vibration to decrease to 0.2 in?
3.1.3 Scalar Formulation Leammny val. To understand the concept of moment of a force and how to calculate it using a scalar formulation. The magnitude of the moment of a force with a magnitude F around a point O is defined as follows:Mo = Fdwhere d is the force's moment arm. The moment arm is the perpendicular distance from the axis at point O to the force's line of action. Figure Part A A stool at a restaurant is anchored to the floor. When a customer is in the process of sitting down, a horizontal force with magnitude F₁ is exerted at the top of the stool support as shown in the figure. (Figure 1) When the customer is seated, a vertical force with magnitude F2 is exerted on the stool support. If the maximum moment magnitude that the stool support can sustain about point A is M₁ = 175 lb-ft, what is the maximum height di that the stool can have if the magnitudes of the two forces are F₁ = 35.0 lb and F₂ = 135 lb ? Assume that moments acting counterclockwise about point A are positive…
The graph of a sinusoidal function has a maximum at (4, 3) followed by a minimum at (8, 1). Which of the following represents the period of the function? O a. 2 . O b. 12 O c. 8 O d. 4

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