question_answer

(i) What is meant by simple harmonic motion (S.H.M.)? (ii) At what points is the energy entirely kinetic and potential in S.H.M.? (iii) What is the total distance travelled by a body executing S.H.M. in a time equal to its time period, if its amplitude is A?                         

Answer:

                (i) Simple harmonic motion. A particle is said to execute simple harmonic motion if it moves to and fro about a mean position under the action of a restoring force which is directly proportional to its displacement from the mean position and is always directed towards the mean position. If the displacement of the oscillating particle from the mean position is small, then \[\text{Restoring}\,\text{force}\propto \,\text{Displacement}\] or \[F\propto x\] or \[F=-k\,x\] where k is positive constant called force constant or spring factor and is defined as the restoring force produced per unit displacement. The negative sign shows that the restoring force always acts in the opposite direction of displacement\[x\]. The above equation defines SHM. (ii) The energy is entirely kinetic at mean position i.e., at \[y=0\]. The energy is entirely potential at extreme positions, i.e., \[y=\pm A.\]  (iii) Total distance travelled in time period T \[=2A+2A=4A.\]