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 (in pounds), g is gravity (in feet), 5 is air resistance, and 120 is spring constant of rope. This equation can be converted into a system of first-order differential equations with initial conditions h(0) = 100 and v(0) = 0, We can do this by letting v = h', Then, the original equation becomes mv' + 5v + 120h = mg, which is a first-order differential equation in v. We also have the equation h' = v, which is a first-order differential equation in h. The solution of this system will give us the height h(t) and velocity v(t) as functions of time t for a given mass m. Please solve this initial value problem using undetermined coefficients or variation of parameters (you may use 85 for m if an m is required for the solution)
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 (in pounds), g is gravity (in feet), 5 is air resistance, and 120 is spring constant of rope. This equation can be converted into a system of first-order differential equations with initial conditions h(0) = 100 and v(0) = 0, We can do this by letting v = h', Then, the original equation becomes mv' + 5v + 120h = mg, which is a first-order differential equation in v. We also have the equation h' = v, which is a first-order differential equation in h. The solution of this system will give us the height h(t) and velocity v(t) as functions of time t for a given mass m. Please solve this initial value problem using undetermined coefficients or variation of parameters (you may use 85 for m if an m is required for the solution)
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