6. Consider the force spring-mass system with a mass of 1 kilogram attached to a spring whose constant is 2 N/m, and the entire system is submerged in a liquid that imparts a damping force numerically equal to 2 times the instantaneous velocity governed by the equation x" + 2x' + 2x=2 sint a. Find the general solution to the differential equation b. Solve the IVP with initial conditions x (0) = 2 and x'(0) = 0 c. Plot the solution and find the time t when the first three equilibrium points for the spring cross the t-axis.
6. Consider the force spring-mass system with a mass of 1 kilogram attached to a spring whose constant is 2 N/m, and the entire system is submerged in a liquid that imparts a damping force numerically equal to 2 times the instantaneous velocity governed by the equation x" + 2x' + 2x=2 sint a. Find the general solution to the differential equation b. Solve the IVP with initial conditions x (0) = 2 and x'(0) = 0 c. Plot the solution and find the time t when the first three equilibrium points for the spring cross the t-axis.
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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Transcribed Image Text:6. Consider the force spring-mass system with a mass of 1 kilogram attached to a spring whose constant is 2 N/m,
and the entire system is submerged in a liquid that imparts a damping force numerically equal to 2 times the
instantaneous velocity governed by the equation
x" + 2x' + 2x = 2 sint
a. Find the general solution to the differential equation
b. Solve the IVP with initial conditions x(0) = 2 and x'(0) = 0
c. Plot the solution and find the time t when the first three equilibrium points for the spring cross the f-axis.
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