11. A 4lb weight stretches a spring 6 inches. The mass is then, released from an initialposition of 4 ft. below the equilibrium position with an initial upward velocity of 24 ft/s.d²x(a) Write the equation of motion as a second order differential equation.(Hint: mdt2-k x)(b) What are the initial conditions representing the motion?(c) Solve the initial value problem given by (a) and (b) to find the equation of motion.(d) Write the equation of motion is sine form.(e) What is the amplitude of motion?(f) What is the period of motion?(g) What is the frequency of motion?

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Answered: 11. A 4lb weight stretches a spring 6…

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 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
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.
dv A model for the velocity v at timetof a certain object faling under the influence cf gravity in a viscous medium is given by the equation 1-. From the direction field shown in the figure to the right, skotch the dt 12 solutions with the initial conditions v(0) = 10, 12, and 19. Why is the value v= 12 calied the "terminal velocity"? Choose the correct skelch of the solutions with the initial conditions v(0) = 10, 12, and 19. O A. OB. Oc.
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Laboratory department detects the concentration C of impurity of an oil purifier changes with time t and is described by the equation = b+ dm - Cm, where b,d,a and m are dt constants. Given C = Co and when t = 0. Solve the equation and show that -mt -mt c = + a][1- e=]+ coe
3. A big slug weighing 10 pounds stretches a spring ½ foot. The slug is removed and replaced by another slug, of mass 1.6 slugs. The slug on the spring is then taken to the bottom of the sea (where the water offers resistance that is approximately equal to the velocity of the object) and then released from a position of 1/3 foot above the equilibrium with an downward velocity of 5/4 feet per second. (a) Set up the DE for this situation and show all the steps to find the position equation for the spring. Use X for the position and t for the time. Round all values to 2 decimal places for simplicity. (b) Graph your equation from (a), labeling the axes, and use your graph to find the second time where the slug is heading downwards and passes equillibrium. Write a sentence to summarize.
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