The figure depicts four $x-t$ plots for the linear motion of a particle. Which of the plots represent periodic motion? What is the period of motion (in case of periodic motion)?

(B AND D) Periodic motion is defined as a motion that repeats itself at regular intervals of time.
$(a)$ This is not a periodic motion. The displacement $x$ increases continuously with time $t$. There is no repetition of the motion.
$(b)$ This is a periodic motion. The particle repeats its motion after every $2 \ s$ (e.g.,from $t = -1 \ s$ to $t = 1 \ s$). The period of motion is $T = 2 \ s$.
$(c)$ This is not a periodic motion. Although the particle returns to the same position,the pattern of motion does not repeat itself in equal intervals of time.
$(d)$ This is a periodic motion. The particle follows a sinusoidal path and repeats its motion after every $2 \ s$ (e.g.,from $t = -1 \ s$ to $t = 1 \ s$). The period of motion is $T = 2 \ s$.