7. A mass weighing 3 lb stretches a spring 3 in. If the mass is pushed upward, contracting the spring a distance of 1in., and then set in motion with a downward velocity of 2 ft/s, and if there is no damping, find the position y of themass at any time t. Determine the frequency, period, amplitude, and phase of the motion.

Given that: Weight = 3 lb Spring stretched = 3 in. Initial position, y(0) = -1 in = -1/12 ft…

Answered: 7. A mass weighing 3 lb stretches a…

Advanced Engineering Mathematics

10th Edition

ISBN:9780470458365

Author:Erwin Kreyszig

Publisher:Erwin Kreyszig

Chapter2: Second-order Linear Odes

Section: Chapter Questions

Problem 1RQ

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13-41. A 150-mm-diameter shaft with a mass of 20 kg is rotating at 900 rpm. A pulley mounted on the shaft has a mass moment of inertia of 0.15 kg - m2. If the shaft and the pulley coast to a stop due to a tangential frictional force of 8 lb at the outer radius of the shaft, determine the time required.
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 catenary cable is one which is hung between two points not in the same vertical line. As depicted in figure(right) it is subject to no loads other than its own weight. Thus, its weight acts as a uniform load per unit length along the cable w (N/m). A free-body diagram of a section AB is depicted in Fig. P6.17b, where TA and Tâ are ... the tension forces at the end. Based on horizontal and verti- cal force balances, the following differential equation model of the cable can be derived: W= ws (a) (b) 2 d²y dx² (dy` 1+ dx w %3D Calculus can be employed to solve this equation for the height of the cable y as a function of distance x: w TA y = cosh х) + yo — w w (a) Use a numerical method to calculate a value for the parameter TA given values for the parameters w = 10 and yo = 5, such that the cable has a height of y = 15 at X=200 The value of Ta is Blank 1. Express your answer in decimal with two decimal digits after the decimal point.
A spring is stretched 8 feet into equilibrium by an object weighing 64 pounds, with a damping force of 8 pounds per ft/sec and an ex ternal force of 24 pounds. If the object is pushed down with a speed of 4ft/sec from a position 1 ft above the equilibrium position, find its displacement.

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