At time $ t = 0 $, an object is released from rest at position $ x = +x_{\text{max}} $ and undergoes simple harmonic motion along the $ x $-axis about the equilibrium position of $ x = 0 $. The period of oscillation of the object is $ T $. Which of the following expressions is equal to the object’s position at time $ t = \dfrac{T}{8} $?

Question

At time $ t = 0 $, an object is released from rest at position $ x = +x_{\text{max}} $ and undergoes simple harmonic motion along the $ x $-axis about the equilibrium position of $ x = 0 $. The period of oscillation of the object is $ T $. Which of the following expressions is equal to the object&#8217;s position at time $ t = \dfrac{T}{8} $?(a) $ \dfrac{x_{\text{max}}}{8} $
, (b) $ \dfrac{x_{\text{max}}}{2} $
, (c) $ \dfrac{x_{\text{max}}}{\sqrt{2}} $
, (d) $ \dfrac{x_{\text{max}}}{\pi} $
, (e) $ \dfrac{x_{\text{max}}}{2\pi} $
:

Jason · Accepted Answer

$\dfrac{x_{\text{max}}}{\sqrt{2}}$

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