6.DETAILS(a) the mass is initially released from rest from a point 1 meter below the equilibrium positionx(0)x'(0)x(t)A 1-kilogram mass is attached to a spring whose constant is 16 N/m, and the entire system is then submerged in a liquid that imparts a damping force numerically equal to 10 times the instantaneousvelocity. Determine the initial conditions and equations of motion if the following is true.=X(t)==ZILLDIFFEQMODAP11 5.1.027.EP.==(b) the mass is initially released from a point 1 meter below the equilibrium position with an upward velocity of 12 m/sX(0)mx'(0)=mm/smMY NOTESm/sASK YOUR TEACHER

Answered: Image /qna-images/answer/9a621336-44f9-4010-b6f0-b72a2cfcafe8.jpg

Answered: 6. DETAILS ZILLDIFFEQMODAP11…

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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(1) The T-shaped bar is loaded with two forces and a moment as shown. The bar is supported by a pin at O and a roller at C. The mass of the bar is negligible. (a) For P = 100 N, determine the normal force at roller C and the magnitude of the reaction at pin O. (b) Determine the maximum load Pmax that can be applied for the T-shaped bar to maintain equilibrium. Ans: (a) Nc=240 N, O=116.6 N (b) Pmax = 260 N A 60 mm 24 N-m D 60 mm 40 mm B 180 N 40 mm
A force of 540 newtons stretches a spring 3 meters. A mass of 45 kilograms is attached to the end of the spring and is initially released from the equilibrium position with an upward velocity of 10 m/s. Give the initial conditions. x(0) x'(0) = x(t) = m m/s Find the equation of motion. m
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 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. A mass that weighs 64 lb stretches a spring 0.8 ft. The mass is attached to a dashpot mechanism that has a damping coefficient of 8 lb s/ft and is acted on by an external force of 60 cos(4t) lb. The mass is set in motion from its equilibrium position with no initial velocity. Let y(t) denote the displacement (in ft) of the mass from its equilibrium position after t seconds. (a) Find an initial-value problem which describes this process. (You may use the fact that g = 32 ft/s' and 1 ft=12 in.) (b) Is the system underdamped, overdamped, or critically damped? Justify your an- swer.
*) Find y as a function of x if y" 11y" + 18y' = 32e*, y(0) = 29, y'(0) = 12, y"(0) = 22. y(x) =
1. A particle moves along the X-axis according to the equation x=2+32, where x is in m and is in second. Calculate the instantaneous velocity and instantaneous acceleration at =3s. 2. When struck by a club, a golf ball initially at rest acquires a speed of 31.0 m/s. If the ball is in contact with the club for 1.17 ms, what is the magnitude of the average acceleration of the ball?
4.4 11 11. A 0.2-kg mass is attached to a spring having a spring constant 5 kg/s2. The system is displaced 0.5 m from its equilibrium position and released from rest. If there is no damping present, find the amplitude, frequency, and phase of the resulting motion. Plot the solution.
1 - Find a formula for the rate of change dv/dt of the volume of a balloon being inflated such that it radius R increases at a rate equal to dR/dt. 2 - Find a formula for the rate of change da/dt of the area A of a square whose side x centimeters changes at a rate equal to 2 cm/sec. 3- Two cars start moving from the same point in two directions that makes 90 degrees at the constant speeds of s1 and s2. Find a formula for the rate of change of the distance D between the two cars.

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