When a mass of 2 kilograms is attached to a spring whose constant is 32 N/m, it comes to rest in the equilibrium position. Starting at t = 0, a force equal to f(t) = 102e-2t cos(4t) is applied to the sy Find the equation of motion in the absence of damping. x(t) = cos (41) + 15 sin (41) + -21 (3 cos (4t) - 3 sin (47)) m

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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When a mass of 2 kilograms is attached to a spring whose constant is 32 N/m, it comes to rest in the equilibrium position. Starting at t = 0, a force equal to f(t) = 102e-2t cos(4t) is applied to the system.
Find the equation of motion in the absence of damping.
15
x(t) = - cos (41) + ¹5 sin (41)
+
-2t
e
- (3 cos ( 4t) — 3 sin ( 4t))
2
X
m
Transcribed Image Text:When a mass of 2 kilograms is attached to a spring whose constant is 32 N/m, it comes to rest in the equilibrium position. Starting at t = 0, a force equal to f(t) = 102e-2t cos(4t) is applied to the system. Find the equation of motion in the absence of damping. 15 x(t) = - cos (41) + ¹5 sin (41) + -2t e - (3 cos ( 4t) — 3 sin ( 4t)) 2 X m
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