Saved Bookmarks
| 1. |
Describe Simple HarmonicMotion as a projection of uniform circular motion. |
|
Answer» Solution :(i) Let us CONSIDER a particle of mass m moving with uniform SPEED v along the circumference of a circle whose radius is r in anti-clockwise direction (as shown in Figure). (ii) It is assumed thatthe oriin with the centre O of the circle. (iii) If `omega` is the ANGULAR displacement of the particle at any instant of time t, then `theta= omegat`.By projecting the uniform circular motion on its diameter a simple harmonic motion is obtained. (iv) This mass that we can associate a map (or a relationship) between uniform circular (or revolution) motion to vibratory motion. (v) Conversely. any vibratory motion or revolution can be mapped touniform circular motion. The position of a particle moving on a circle is projected on to its vertical diameter or on to a line parallel to vertical diameter. (vi) Similarly, we can do it for horizontal axis or a line parallel to horizontal axis. Example : Let us consider a spring mass system (or oscillation of pendulum) as shown in figure. When the spring moves up and down (or pendulum moves to and fro), the motion of the mass of bob is mapped to points on the circular motion of the circular motion.  THUS, if a particle undergoes uniform circular motion then the projection of the particle on the diameter of the circle (or on a line paralle to the diameter) traces straightline motion that is simpleharmonic in nature. The circle is known as reference circle of the simple harmonic motion. |
|