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- https://math.libretexts.org/Bookshelves/Differential_Equations/Differential_Equations_for_Engineers_(Lebl)/2%3A_Higher_order_linear_ODEs/2.6%3A_Forced_Oscillations_and_ResonanceLet us consider to the example of a mass on a spring. We now examine the case of forced oscillations, which we did not yet handle.
- https://math.libretexts.org/Courses/De_Anza_College/Introductory_Differential_Equations/05%3A_The_Laplace_Transform/5.03%3A_ConvolutionThis page discusses the use of inverse Laplace transforms and convolution in solving ordinary differential and Volterra integral equations. It highlights the simplification of computations through the...This page discusses the use of inverse Laplace transforms and convolution in solving ordinary differential and Volterra integral equations. It highlights the simplification of computations through these methods. An example is provided where a differential equation involving an integral is transformed into the frequency domain, resulting in the expression \( X(s) = \dfrac{s-1}{s^2-2} \). The final solution is obtained as \( x(t) = \cosh(\sqrt{2}\, t) - \dfrac{1}{\sqrt{2}} \sinh(\sqrt{2}\,t) \).
- https://math.libretexts.org/Courses/De_Anza_College/Introductory_Differential_Equations/03%3A_Higher_order_linear_ODEsIn this chapter, we go a little further and look at second-order equations, which are equations containing second derivatives of the dependent variable. The solution methods we examine are different f...In this chapter, we go a little further and look at second-order equations, which are equations containing second derivatives of the dependent variable. The solution methods we examine are different from those discussed earlier, and the solutions tend to involve trigonometric functions as well as exponential functions. Here we concentrate primarily on second-order equations with constant coefficients.
- https://math.libretexts.org/Courses/East_Tennesee_State_University/Book%3A_Differential_Equations_for_Engineers_(Lebl)_Cintron_Copy/2%3A_Higher_order_linear_ODEs/2.6%3A_Forced_Oscillations_and_ResonanceLet us consider to the example of a mass on a spring. We now examine the case of forced oscillations, which we did not yet handle.
- https://math.libretexts.org/Courses/Coastline_College/Math_C285%3A_Linear_Algebra_and_Diffrential_Equations_(Tran)/14%3A_Higher_order_linear_ODEs/14.10%3A_Forced_Oscillations_and_ResonanceLet us consider to the example of a mass on a spring. We now examine the case of forced oscillations, which we did not yet handle.
- https://math.libretexts.org/Courses/Lake_Tahoe_Community_College/MAT-204%3A_Differential_Equations_for_Science_(Lebl_and_Trench)/04%3A_Higher_order_linear_ODEs/4.10%3A_Forced_Oscillations_and_ResonanceLet us consider to the example of a mass on a spring. We now examine the case of forced oscillations, which we did not yet handle.
- https://math.libretexts.org/Bookshelves/Differential_Equations/Applied_Linear_Algebra_and_Differential_Equations_(Chasnov)/03%3A_III._Differential_Equations/08%3A_Second-Order_ODEs_Constant_Coefficients/8.07%3A_ResonanceResonance occurs when the frequency of the inhomogeneous term matches the frequency of the homogeneous solution.
- https://math.libretexts.org/Courses/De_Anza_College/Introductory_Differential_Equations/03%3A_Higher_order_linear_ODEs/3.10%3A_Forced_Oscillations_and_ResonanceLet us consider to the example of a mass on a spring. We now examine the case of forced oscillations, which we did not yet handle.
