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Linear Algebra: A Modern Introduction

Linear Algebra: A Modern Introduction

4th Edition

ISBN:9781285463247

Author:David Poole

Publisher:David Poole

Chapter6: Vector Spaces

Section6.7: Applications

Problem 18EQ

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Q2 (a) A mass-spring system shown in Figure Q2(a) has a spring coefficient of k = 6 N/mm and a
damping coefficient of c = 0.5 Ns/mm. The mass is m = 0.5 kg. A continuous force F(t)
3e³t is exerted on the mass to induce oscillation. The system is modeled by the following
differential equation:
- (=/=) y = F(t)
y" +
Using the method of undetermined coefficient, find the displacement of the mass with
respect to time, y(t).
(10 marks)
(b) Solve the following second order differential equation using the method of variation of
parameters:
y" - 16y=
Xx
e4x
(10 marks)

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