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3. Find the general solution of the differential equation y(4) - 4y" = t² + et.

3. Find the general solution of the differential equation y(4) - 4y" = t² + et.

Advanced Engineering Mathematics
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. Supposed that a mass weighing 10 lbs. stretches a spring 2 inches. If the mass is displaced additional 2 inches, and is then set in motion with an initial upward velocity of 1 ft/sec, determine the position of the mass at any later time. Also, determine the period, amplitude, and phase angle of the motion. 2. A mass weighing 4 lbs. stretches a spring 1.5 inches. The mass is given a positive displacement of 2 inches from its equilibrium position and released with no initial velocity. Assuming that there is no damping and that the mass is acted on by an external force of 2 cos 3t lbs., formulate the IVP describing the motion of the mass. What is the position of the mass at any time t? Determine also the period and amplitude of motion of the mass. 3. Find the general solution of the differential equation y(4) - 4y" = t² + et.
Transcribed Image Text:1. Supposed that a mass weighing 10 lbs. stretches a spring 2 inches. If the mass is displaced additional 2 inches, and is then set in motion with an initial upward velocity of 1 ft/sec, determine the position of the mass at any later time. Also, determine the period, amplitude, and phase angle of the motion. 2. A mass weighing 4 lbs. stretches a spring 1.5 inches. The mass is given a positive displacement of 2 inches from its equilibrium position and released with no initial velocity. Assuming that there is no damping and that the mass is acted on by an external force of 2 cos 3t lbs., formulate the IVP describing the motion of the mass. What is the position of the mass at any time t? Determine also the period and amplitude of motion of the mass. 3. Find the general solution of the differential equation y(4) - 4y" = t² + et.
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