A given scenario of a person falling into a pit attached to a rope can be modeled by the second-order non-homogeneous differential equation mh'' + 5h' + 120h = mg where m is mass of person and g is gravity. This equation can be converted into a system of first-order differential equations with initial conditions h(0) = 100 and v(0) = 0. How do we find out if the system has any equilibrium points and how do we verify our answer?

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