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Physics-

General

Easy

Question

The $x$ - $t$ graph of a particle undergoing simple harmonic motion is shown below. The acceleration of the particle at $t equals fraction numerator 4 over denominator 3 end fraction$ s is

$\frac{\sqrt{3}}{32} π^{2} c m s^{- 2}$
$- \frac{π^{2}}{32} c m s^{- 2}$
$\frac{π^{2}}{32} c m s^{- 2}$
$- \frac{\sqrt{3}}{32} π^{2} c m s^{- 1}$

The correct answer is: $negative fraction numerator square root of 3 over denominator 32 end fraction pi to the power of 2 end exponent c m s to the power of negative 1 end exponent$

$T equals 8 s comma blank omega equals fraction numerator 2 pi over denominator T end fraction equals open parentheses fraction numerator pi over denominator 4 end fraction close parentheses r a d s to the power of negative 1 end exponent$
$x equals A sin invisible function application omega blank t$
$therefore blank a equals negative omega to the power of 2 end exponent x equals blank minus open parentheses fraction numerator pi to the power of 2 end exponent over denominator 16 end fraction close parentheses sin invisible function application open parentheses fraction numerator pi over denominator 4 end fraction t close parentheses$
Substituting $t equals fraction numerator 4 over denominator 3 end fraction$ s, we get
$a equals blank minus open parentheses fraction numerator square root of 3 over denominator 32 end fraction pi to the power of 2 end exponent close parentheses c m s to the power of negative 2 end exponent$

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