MCQ
A particle oscillates along the $x$-axis according to the law, $x(t)=x_0 \sin ^2\left(\frac{t}{2}\right)$ where $x_0=1 m$. The kinetic energy ( K ) of the particle as a function of $x$ is correctly represented by the graph.
- ✓
- B
- C
- D
✓
Answer
Correct option: A.
(A)
Sol. $\quad x = x _0 \sin ^2 \frac{ t }{2}= x _0\left(\frac{1-\cos t }{2}\right)$
$
x-\frac{x_0}{2}=\frac{-\cos t}{2}
$
where $x_0=1$
$
x-\frac{1}{2}=\frac{-\cos t}{2}
$
Particle is oscillating between $x =0$ to $x =1$
Sol. $\quad x = x _0 \sin ^2 \frac{ t }{2}= x _0\left(\frac{1-\cos t }{2}\right)$
$
x-\frac{x_0}{2}=\frac{-\cos t}{2}
$
where $x_0=1$
$
x-\frac{1}{2}=\frac{-\cos t}{2}
$
Particle is oscillating between $x =0$ to $x =1$
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