A body of mass 2kg is dropped in free fall starting from rest. Suppose there is air resistance R = 5v, where v is the speed with which it falls said object. If x(t) represents the position of the object at any instant, the equation that models the position is given by: 2x′′+ 5x′= 19.6. a) Solve the homogeneous equation 2x′′+ 5x′= 0. b) Solve the differential equation 2x′′+ 5x′= 19.6 using undetermined coefficients subject to the conditions x(0) = 0 and x′(0) = 0 (since it starts from rest).
A body of mass 2kg is dropped in free fall starting from rest. Suppose there is air resistance R = 5v, where v is the speed with which it falls said object. If x(t) represents the position of the object at any instant, the equation that models the position is given by: 2x′′+ 5x′= 19.6. a) Solve the homogeneous equation 2x′′+ 5x′= 0. b) Solve the differential equation 2x′′+ 5x′= 19.6 using undetermined coefficients subject to the conditions x(0) = 0 and x′(0) = 0 (since it starts from rest).
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 body of mass 2kg is dropped in free fall starting from rest.
Suppose there is air resistance R = 5v, where v is the speed with which it falls
said object. If x(t) represents the position of the object at any instant, the equation
that models the position is given by:
2x′′+ 5x′= 19.6.
a) Solve the homogeneous equation 2x′′+ 5x′= 0.
b) Solve the
subject to the conditions x(0) = 0 and x′(0) = 0 (since it starts from rest).
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