1. (а) A spring with spring constant 12 pounds per foot is attached to the ceiling. A 4 pound weight is attached. The mass-spring system is set in motion in a medium that imparts a damping force numerically equal to 2 times the velocity. The mass is pushed up three inches from the equilibrium position and given a downward velocity of 2 feet per second. Write down the initial value problem for the position, x(t), as a function of time, t. (Б) Solve the IVP you formed in part (a). Suppose the same spring-mass system is now attached to a movable plank, which moves like the (c) function 5 sin 2t for all t > 0. Adjust the initial value problem you wrote in part (a) to include this fact. Do not solve!
1. (а) A spring with spring constant 12 pounds per foot is attached to the ceiling. A 4 pound weight is attached. The mass-spring system is set in motion in a medium that imparts a damping force numerically equal to 2 times the velocity. The mass is pushed up three inches from the equilibrium position and given a downward velocity of 2 feet per second. Write down the initial value problem for the position, x(t), as a function of time, t. (Б) Solve the IVP you formed in part (a). Suppose the same spring-mass system is now attached to a movable plank, which moves like the (c) function 5 sin 2t for all t > 0. Adjust the initial value problem you wrote in part (a) to include this fact. Do not solve!
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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Question
Pls answer question 1 part C
Transcribed Image Text:1. (а)
A spring with spring constant 12 pounds per foot is attached to the ceiling. A 4 pound weight is
attached. The mass-spring system is set in motion in a medium that imparts a damping force numerically
equal to 2 times the velocity. The mass is pushed up three inches from the equilibrium position and given
a downward velocity of 2 feet per second. Write down the initial value problem for the position, x(t), as a
function of time, t.
(b)
Solve the IVP you formed in part (a).
Suppose the same spring-mass system is now attached to a movable plank, which moves like the
function 5 sin 2t for all t > 0. Adjust the initial value problem you wrote in part (a) to include this fact. Do
not solve!
2.
Find two linearly independent power series solutions of the differential equation
(x+ 2)y" + xy' – y = 0.
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