Lecture 9 Notes

Examples position of object in one dimensional space

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Unformatted text preview: ￿ x =v Introduction to systems of equations • So far, we’ve only dealt with equations with one unknown function. Sometimes, we’ll be interested in more than one unknown function. • Examples: • position of object in one dimensional space in terms of x, v: mx￿￿ + γ x￿ + kx = 0 → mv ￿ + γ v + kx = 0 γ k ￿ ￿ x =v v =− v− x m m ￿￿ ￿ x =v Introduction to systems of equations • So far, we’ve only dealt with equations with one unknown function. Sometimes, we’ll be interested in more than one unknown function. • Examples: • position of object in one dimensional space in terms of x, v: mx￿￿ + γ x￿ + kx = 0 → mv ￿ + γ v + kx = 0 γ k ￿ ￿ x =v v =− v− x m m ￿￿ ￿ x =v x￿ = v k γ v =− x− v m m ￿ Introduction to systems of equations • So far, we’ve only dealt with equations with one unknown function. Sometimes, we’ll be interested in more than one unknown function. • Examples: • position of object in one dimensional space in terms of x, v: mx￿￿ + γ x￿ + kx = 0 → mv ￿ + γ v + kx = 0 γ k ￿ ￿ x =v v =− v− x m m ￿￿ ￿ x =v x￿ = v k γ v =− x− v m m ￿ ￿ ￿￿ ￿ 0 x = k v −m ￿￿ ￿ 1 x γ v −m Introduction to systems of equations • So far, we’ve only dealt with equations with one unknown function. Sometimes, we’ll be interested in more than one unknown function. • Examples: • position of object in one dimensional space in terms of x, v. Introduction to systems of equations • So far, we’ve only dealt with equations with one unknown function. Sometimes, we’ll be interested in more than one unknown function. • Examples: • position of object in one dimensional space in terms of x, v. • position of an object in a plane (x, y coordinates) or three dimensional space (x, y, z coordinates). Introduction to systems of equations • So far, we’ve only dealt with equations with one unknown function. Sometimes, we’ll be interested in more than one u...
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