Question 59: Oscillations

Question

A particle oscillates along the $x$-axis according to the law, $x(\mathrm{t})=x_0 \sin ^2\left(\frac{\mathrm{t}}{2}\right)$ where $x_0=1 \mathrm{~m}$. The kinetic energy $(\mathrm{K})$ of the particle as a function of $x$ is correctly represented by the graph

Accepted Answer

$$\begin{aligned}
& x=x_0 \sin ^2 \frac{t}{2}=x_0\left(\frac{1-\cos t}{2}ight) \
& x-\frac{x_0}{2}=\frac{-\cos t}{2} \
& 	ext { where } x_0=1 \
& x-\frac{1}{2}=\frac{-\cos t}{2}
\end{aligned}$$
Particle is oscillating between $\mathrm{x}=0$ to $\mathrm{x}=1$

Answer

Answer

Answer

Answer

Oscillations

A particle oscillates along the x-axis according to the law, x(\mathrm{t})=x_0 \sin ^2\left(\frac{\mathrm{t}}{2}\right) where x_0=1 \mathrm{~m}. The kinetic energy (\mathrm{K}) of the particle as a function of x is correctly represented by the graph

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