A particle osacillates along the x-axis according to the law, where . The kinetic energy (K) of the particle as a function of x is correctly represented by the graph. [2025]

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Solution

Q.
A particle oscillates along the x-axis according to the law, $x (t) = x_{0} \sin^{2} (\frac{t}{2})$ where $x_{0} = 1 m$ . The kinetic energy (K) of the particle as a function of x is correctly represented by the graph. [2025]

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Ans.
(1)

$x (t) = x_{0} \sin^{2} (\frac{t}{2}) = \frac{x_{0}}{2} (1 - \cos t)$

Clearly $\frac{x_{0}}{2}$ is mean position, Particle is oscillating between

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