JEE Main 2018 — Ray Optics Question with Solution

A particle is oscillating on the $\mathrm{X}$-axis with an amplitude $2\mathrm{cm}$ about the point $x_0=10\mathrm{cm}$ with a frequency $\omega$. A concave mirror of focal length 5 $\mathrm{cm}$ is placed at the origin (see figure) Identify the correct statements: (A) The image executes periodic motion (B) The image executes non-periodic motion (C) The turning points of the image are asymmetric w.r.t the image of the point at $x$ $=10\mathrm{cm}$ (D) The distance between the turning points of the oscillation of the image is $\frac{100}{21}$