A particle oscillates along the x-axis according to the law, x(t) = x0 sin^2 (t / 2)

Question

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

(1)

(2)
 

(3)

(4)

Answer 1

Correct option is : (1)

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

\(x-\frac{x_{0}}{2}=\frac{-\cos t}{2}\) 

where \(\mathrm{x}_{0}=1\) 

\( x-\frac{1}{2}=\frac{-\cos t}{2}\)

Particle is oscillating between \(\mathrm{x}=0\) to \(\mathrm{x}=1\)