9. A 1 kg mass is attached to a spring with constant 13 N/m. The system is immersed in amedium which offers a damping force numerically equal to 6 times the instantaneous velocity.If x is the displacement of the mass from equilibrium, measured in meters,then x′′ + 6x′ + 13x = 0 . Which of the following statements is true?A. x(t) = c1e^−t + c2e^−5t, and the system is underdamped.B. x(t) = c1e^−t + c2e^−5t, and the system is overdamped.C. x(t) = c1e^−3t cos(2t) + c2e^−3t sin(2t), and the system is underdamped.D. x(t) = c1e^−3t cos(2t) + c2e^−3t sin(2t), and the system is overdamped.

9. A 1 kg mass is attached to a spring with constant 13 N/m. The system is immersed in amedium which offers a damping force numerically equal to 6 times the instantaneous velocity.If x is the displacement of the mass from equilibrium, measured in meters,then x′′ + 6x′ + 13x = 0 . Which of the following statements is true?A. x(t) = c1e^−t + c2e^−5t, and the system is underdamped.B. x(t) = c1e^−t + c2e^−5t, and the system is overdamped.C. x(t) = c1e^−3t cos(2t) + c2e^−3t sin(2t), and the system is underdamped.D. x(t) = c1e^−3t cos(2t) + c2e^−3t sin(2t), and the system is overdamped.

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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Question

9. A 1 kg mass is attached to a spring with constant 13 N/m. The system is immersed in a
medium which offers a damping force numerically equal to 6 times the instantaneous velocity.
If x is the displacement of the mass from equilibrium, measured in meters,
then x′′ + 6x′ + 13x = 0 . Which of the following statements is true?
A. x(t) = c1e^−t + c2e^−5t, and the system is underdamped.
B. x(t) = c1e^−t + c2e^−5t, and the system is overdamped.
C. x(t) = c1e^−3t cos(2t) + c2e^−3t sin(2t), and the system is underdamped.
D. x(t) = c1e^−3t cos(2t) + c2e^−3t sin(2t), and the system is overdamped.

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