A 1-kg mass is attached to a spring whose constant is 16N/m, and the entire system is then submerged in a liquid that imparts a damping force numerically equal to 10 times theinstantaneous velocity. Deterrmine the equation of motion if the mass is initially released from rest from a point 1 m below the equilibrium position.1-8te-2tu(t) =4-2t1e-8t1-8tе-2t4ult) = - 3e1-8t-2t +

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Answered: A 1-kg mass is attached to a spring…

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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A mass weighing 32 lb is attached to a spring hanging from the ceiling and comes to rest at its equilibrium position. At time t= 0, an external force of F(t) = 3 cos 2t Ib is applied to the system. If the spring constant is 15 Ib/ft and the damping constant is 2 Ib-sec/ft, find the steady-state solution for the system. Use g = 32 ft / sec". The steady-state solution is y(t) =|.
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Suppose a 10-lb object stretches a spring 2.25 feet while in equilibrium. If the object is displaced an additional 1 inches and is then set in motion with an initial upward velocity of -0.7 feet per second. Use 1 slug = 32 lbs. Your answer is partially correct. (i) For what values of a, ß, and y is this spring-mass system expressed as the following initial value problem, where u (t) is the position of the object at any time t: α = eTextbook and Media ,B = = u" + au = 0, u (0) = ß, u' (0) = y? , Y = = -0.7
Find the solution to the Initial Value Problem describing the horizontal motion of a mass attached to a spring, mx = -k(x - 1), x(0)=4, x(0) = 0, for m 1, k = 9, 14. Describe in words the motion of the mass.
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Pls answer question 1 part B
A mass weighing 16 lb stretches a spring 1/4 feet. The mass is attached to a viscous damper with a damping constant of 2 lb-s/ft and is set in motion from its equilibrium position with a downward velocity of 1/2 ft/s. a) Set up the initial value problem (differential equation). b) Solve the equation to find the position of the mass y at any time t. c) Determine when the mass first returns to its equilibrium position. Assume that the y-axis is directed downward.
8 A mass weighing 16 pounds stretches a spring feet. The mass is initially released from rest from a point 2 feet below the equilibrium position, and the subsequent motion takes place in a medium that offers a damping force that is numerically equal to the instantaneous velocity. Find the equation of motion x(t) if the mass is driven by an external force equal to f(t) = 20 cos(3t). (Use g = 32 ft/s² for the acceleration due to gravity.) 2 (√4) x(1) - e -(5) [ - 14 cos (1) ( (VT),) - 134 sin(e) ((7),)] + 20 cos (3) +- 20 sin (38) = е 3 2 3√4t 2 3 3 ft
A spring is pulled back 4cm below its equilibrium point and then released. If the spring has a period of 3 seconds, which of the following models the position of this spring after t seconds? Select one: O a. s()– 3sin:) O b. (21 s(?) = - 3cos :) 21 s(t) = - 4sin O d. s(t): = -4cos
A spring mass system consists of a spring with spring constant k and an attached block of mass m is submerged in a liquid that produces a damping force Fr. m = 2 KG K = 36 N/m Fr 18 times the velocity of the center of mass of the block. = If the mass is initially released from rest 1m below the equilibrium position: Enter your answer in lower case, ex x"+ax'+bx=0 a. "The second degree equation that describe the motion of the center of mass of the attached block is b. The initial conditions are x(0)= c. The Arbitrary Constants that satisfy the IC's are C= the order does not matter" , x'(0)= C=
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