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calculus to solve for total energy: Then finally by noting that 𝑥̇𝑑𝑡 =𝑑𝑥 and using v for speed, we can write: Equation 5 This is the familair expression for total energy! Where kinetic energy (KE) is equal to ½mv² and potential energy (PE) is equal to -∫F ·dx: Equation 6