# Suppose a spring has mass m and spring constant k and let \omega = \sqrt{\frac{k}{m}} ....

## Question:

Suppose a mass {eq}m {/eq} is attached to a spring with spring constant {eq}k {/eq} and let {eq}\omega = \sqrt{\frac{k}{m}} {/eq}. Suppose that the damping constant is so small that the damping is negligible. If an external force {eq}F(t) = F_0 \cos(\omega_0 t) {/eq} is applied, where {eq}\omega_0 \neq \omega {/eq}, use the method of undetermined coefficients to find the equation that describes the motion of the mass.

## Inhomogeneous Linear Differential Equations:

If both {eq}p_2(t) {/eq} and {eq}q(t) {/eq} are not the zero function, then the equation {eq}p_2(t)y''+p_1(t)y'+p_0(t)y=q(t) {/eq} is called a second-order linear inhomogeneous differential equation. The equation {eq}p_2(t)y''+p_1(t)y'+p_0(t)y=0 {/eq} is its associated homogeneous equation, and the function {eq}q(t) {/eq} is the inhomogeneous term of that equation.

If {eq}y_p {/eq} is a particular solution to an inhomogeneous equation, then any other solution {eq}y {/eq} to that equation can be written as {eq}y=y_p+y_h {/eq}, where {eq}y_h {/eq} is some solution to the associated homogeneous equation

## Answer and Explanation: 1

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If a spring with spring constant {eq}k {/eq} has a mass {eq}m {/eq} attached to it, with negligible damping and an applied force {eq}F(t) {/eq},...

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#### Learn more about this topic: Hooke's Law & the Spring Constant: Definition & Equation

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Chapter 4 / Lesson 19
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After watching this video, you will be able to explain what Hooke's Law is and use the equation for Hooke's Law to solve problems. A short quiz will follow.