Q3 of 31 Page 358

Fig. 14.23 depicts four x-t plots for linear motion of a particle. Which of the plots represent periodic motion? What is the period of motion (in case of periodic motion)?

A periodic motion is the one performed by particles oscillating back and forth at regular intervals.


Here, in x-t plots it is seen,


(a) As the time proceeds, the particle continues to proceed with increasing distance without oscillating. Hence, the motion is non-periodic. (Refer Fig 14.23-(a))


(b) The particle vibrates back and forth continuously, producing a periodic motion with a time period of 2 seconds. (Refer Fig 14.23-(b))


(c) The motion is non-periodic as seen in the graph. (Refer Fig 14.23-(c))


(d) The motion is periodic with a period of 2 seconds. (Refer Fig 14.23-(d))



More from this chapter

All 31 →
1

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.

 2

Which of the following examples represent (nearly) simple harmonic motion and which represent periodic but not simple harmonic motion?

(a) the rotation of earth about its axis.


(b) motion of an oscillating mercury column in a U-tube.


(c) motion of a ball bearing inside a smooth curved bowl, when released from a point slightly above the lower most point.


(d) general vibrations of a polyatomic molecule about its equilibrium position.

 4

Which of the following functions of time represent (a) simple harmonic, (b) periodic but not simple harmonic, and (c) non-periodic motion? Give period for each case of periodic motion (ω is any positive constant):

(a) sin ωt – cos ωt


(b) sin3 ωt


(c) 3 cos (π/4 – 2ωt)


(d) cos ωt + cos 3ωt + cos 5ωt


(e) exp (–ω2t2)


(f) 1 + ωt + ω2t2

5

A particle is in linear simple harmonic motion between two points, A and B, 10 cm apart. Take the direction from A to B as the positive direction and give the signs of velocity, acceleration and force on the particle when it is

(a) at the end A,


(b) at the end B,


(c) at the mid-point of AB going towards A,


(d) at 2 cm away from B going towards A,


(e) at 3 cm away from A going towards B, and


(f) at 4 cm away from B going towards A.