Which concepts are needed for the description of a periodic motion?

$A$ particle moves in the $x-y$ plane according to the equation $\overrightarrow{r} = (\widehat{i} + 2\widehat{j}) A \cos \omega t$. The motion of the particle is:

$A$ body is executing simple harmonic motion of amplitude $a$ and period $T$ about the equilibrium position $x=0$. Large numbers of snapshots are taken at random of this body in motion. The probability of the body being found in a very small interval $x$ to $x+|dx|$ is highest at

What is displacement? Explain its general meaning by giving examples.

$A$ particle is executing simple harmonic motion with an amplitude of $2 \,m$. The difference in the magnitudes of its maximum acceleration and maximum velocity is $4$. The time-period of its oscillation and its velocity when it is $1 \,m$ away from the mean position are respectively:

Which of the following examples represent periodic motion?
$(a)$ $A$ swimmer completing one (return) trip from one bank of a river to the other and back.
$(b)$ $A$ freely suspended bar magnet displaced from its $N-S$ direction and released.
$(c)$ $A$ hydrogen molecule rotating about its centre of mass.
$(d)$ An arrow released from a bow.