Oscillator equation A mechanical oscillator (such as a mass ona spring or a pendulum) subject to frictional forces satisfies theequation (called a differential equation)y″(t) + 2y′(t) + 5y(t) = 0,where y is the displacement of the oscillator from its equilibrium position. Verify by substitution that the functiony(t) = e-t(sin 2t - 2 cos )t2 satisfies this equation.
Oscillator equation A mechanical oscillator (such as a mass ona spring or a pendulum) subject to frictional forces satisfies theequation (called a differential equation)y″(t) + 2y′(t) + 5y(t) = 0,where y is the displacement of the oscillator from its equilibrium position. Verify by substitution that the functiony(t) = e-t(sin 2t - 2 cos )t2 satisfies this equation.
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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Oscillator equation A mechanical oscillator (such as a mass on
a spring or a pendulum) subject to frictional forces satisfies the
equation (called a
y″(t) + 2y′(t) + 5y(t) = 0,
where y is the displacement of the oscillator from its equilibrium position. Verify by substitution that the function
y(t) = e-t
(sin 2t - 2 cos )t2 satisfies this equation.
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