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 does the solution of this system vary for different masses m? In other words, how will the height h(t) and velocity v(t) change as we increase m?

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 does the solution of this system vary for different masses m? In other words, how will the height h(t) and velocity v(t) change as we increase m?

Calculus For The Life Sciences

2nd Edition

ISBN:9780321964038

Author:GREENWELL, Raymond N., RITCHEY, Nathan P., Lial, Margaret L.

Publisher:GREENWELL, Raymond N., RITCHEY, Nathan P., Lial, Margaret L.

Chapter11: Differential Equations

Section11.1: Solutions Of Elementary And Separable Differential Equations

Problem 59E: According to the solution in Exercise 58 of the differential equation for Newtons law of cooling,...

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