Total mechanical energy of a mass oscillating on an ideal spring (12-21)

Question 1 of 5

Question

$\textbf{Total mechanical energy}$ of the oscillating mass–spring system

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Question

$\textbf{Spring constant}$

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Question

$\textbf{Amplitude}$ of the oscillation

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Question

During the oscillation, the kinetic energy $K$ and spring potential energy $U_{\mathrm{spring}}$ both change…

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Question

…but their sum, the total mechanical energy $E$ , always has the same value.

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Review

Equation 12-20 looks like a complicated function of time. But we can simplify it thanks to an important result from trigonometry:

$sin^2\theta + cos^\theta = 1$ for any value of $\theta$