# Oscillatory Motion, Oscillation

Suspend a stone or a marble with the help of a string and tie the other end firmly and allow it to oscillate to and frow and observe. After some time it comes to rest. This position or the body is called its position of equilibrium. when the body is made to oscillate you observe that first it moves in one direction. then It returns and gets displaced in the opposite direction. Again It gets displaced in Its first direction. This motion is repeated for some time. After some time it comes to its equilibrium position. Such a type of motion is called oscillatory motion.

Let us consider the oscillatory moiion of a bob. Let A be its position of equilibrium. Let B and C be its maximum displacements in opposite directions. Let it start from A and go to B. From B it returns, passes A and reaches C. Again it changes its direction at c. passes the position A and goes to B. These motions contiune for some time. When the body which started its motion from A to B again passes A in the same direction. it is said to have completed one oscillation.

Remember : In case of oscillatory motions a body is said tfumplete one oscilliation. when it passes through any point in one direction and passes it tie second time in the same direction

The time displacement graph of oscillatory motion is shown in the figure. Time is represented on the X-axis and displacement on the Y-axis. The graph in the figure represents one oscillation of the body. The intersection of the curve and the X-axis represents Zero displacement. |

You know that the desplacement becomes zero only when the body is in its equilibrium position. PQ and RS are the maximum displacements of the body. You already know the characteristics of an oscillatory motion. 'A' represents equilibrium position of the body. The displacement of the body when it is at A is nil. It is represented by point x on the graph. When the body reaches B the displacement that direction is maximum.

## Oscillation

On the graph it is represented by PQ. After reaching B the body moves in the opposite direction and reaches A. its displacement is nil. It is represented by point y the graph. The body. continues to move and reaches C after crossing A. This is the maximum displacement in the direction opposite to AB. This is denoted by RS on the graph. since it is in the opposite direction of the first displacement it is represented below the X-axjs.

The maximum displacement of the oscillating body from its equilibrium position is called amplitude of the oscillation. The time taken by the body to ececute or perform one oscillation is called period of oscillation. The number of oscillations in unit time Is Falled frequency of oscillation. The unit of frequency in SI system is hertz. 1 Hz = 1 CPS (one cycle per second.) Here cycle means one complete oscillation.