A 1-kilogram mass is attached to a spring whose constant is 21 N/m, and the entire system is then submerged in a liquid that imparts a damping force numerically equal to 10 times the instantaneous velocity.Determine the equations of motion if the following is true.(a) the mass is initially released from rest from a point 1 meter below the equilibrium position7 -3t 3 -7tx(t) =4(b) the mass is initially released from a point 1 meter below the equilibrium position with an upward velocity of 11 m/s-7t1 -3t4x(t) =-Need Help?e +Read It4eWatch ItXm

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Answered: A 1-kilogram mass is attached to 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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デジタル形式で段階的に解決ありがとう!! SOLVE STEP BY STEP IN DIGITAL FORMAT 3. A cylinder of 2 feet in diameter floats with its axis in a vertical position in water with a density of 62.4lb/ft.³. If it dives a little and then releases, its oscillation period is 1.9 seconds. What is the weight of the cylinder? (Remember 2 Newton's law and Archimides principle)
High-speed elevators function under two limitations: (1) the maximum magnitude of vertical acceleration that a typical human body can experience without discomfort is about 1.2 m/s², and (2) the typical maximum speed attainable is about 8.8 m/s. You board an elevator on a skyscraper's ground floor and are transported 190 m above the ground level in three steps: acceleration of magnitude 1.2 m/s² from rest to 8.8 m/s, followed by constant upward velocity of 8.8 m/s. then deceleration of magnitude 1.2 m/s² from 8.8 m/s to rest. T Part A Determine the elapsed time for each of these 3 stages. Express your answers using two significant figures separated by commas. tace, tconstant, tdec = Submit Part B AFN,acc AFN,constant FN FN Submit Request Answer 2 [5] ΑΣΦ Determine the change in the magnitude of the normal force, expressed as a % of your normal weight during each stage. Express your answers using two significant figures separated by commas. 2 AFN,dec FN Request Answer Part C Complete…
3. A simple pendulum is a weight on the end of a string or rod, which when given an initial push, swings back and forth under the influence of gravity. The period T of a pendulum is the time taken for two swings (left to right and back again). The formula for the period is T = 27 dT (a) Find d 9 where is the length of the pendulum (in meters) and g is the acceleration due to gravity (in m/sec2). Note that g is a positive constant. lo zulev lie (x)) (8) (b) When the length of the pendulum increases, does the period increase or decrease? Justify your answer. (0) al bar nob
A force of 720 newtons stretches a spring 4 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 6 m/s. Give the initial conditions. x(0) = x'(0) = Find the equation of motion. x(t) = Need Help? m m/s Read It Watch It
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C (a) Write down the equation of motion for the point particle of mass m moving in the Kepler potential U(x) = -A/x+B/x² where x is the particle displacement in m. (b) Introduce a dissipative term in the equation of motion assuming that the dissipative force acting on a particle is proportional to the partical velocity with the coefficient of proportionality v. Write down the modified equation of motion. From the dimensionless equation of motion modified by dissipation Compare to question (2 b) derive a linearised equation of motion around a stable equilibrium state. Solve it and determine what is the range of values of the free parameter B for which the particle motion is oscillatory or non-oscillatory? What is the critical value of that determines a transition from the subcritical case with the oscillatory motion to the super-critical case with the non-oscillatory motion?
*) Find y as a function of x if y" 11y" + 18y' = 32e*, y(0) = 29, y'(0) = 12, y"(0) = 22. y(x) =

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