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Understanding Physics Topics is essential for solving complex problems in many fields, including engineering and medicine.
What is the Definition of Oscillatory Motion?
Definition: Any motion, which repeats itself at regular intervals of time, is known as periodic motion.
The motion of planets around the sun, the hands of a clock, the blades of a revolving electric fan are some examples of periodic motion. A characteristic of this motion is that, each moves along a definite circular or elliptical path repeatedly in a regular time interval. The motion along an elliptical path is called elliptical or orbital periodic motion, while the other motions are called rotational periodic motion.
On the other hand, if the bob of a simple pendulum is pulled aside slightly and then released, it swings to the other side passing through its equilibrium position. On its way back, the bob again passes through its equilibrium position and returns to its point of release. Then it goes on repeating this to and fro motion.
Thus the bob covers a definite path repeatedly. If the angular displacement of oscillation of the pendulum is less than 40, the amplitude or range of oscillation is small compared to the radius of curvature of the oscillatory path and so the path of the bob may be taken as a straight line. Hence, this motion is called linear periodic motion. The motion of an elastic spring and that of a Piston in the cylinder of an automobile engine are examples of linear periodic motion.
Oscillation or Vibration
If a body undergoing periodic motion has an equilibrium position somewhere inside its path, it experiences no net external force at that point. Hence, if it is left there at rest, it remains there forever. Now, if the body is given a small displacement from the equilibrium position, a restoring force comes into play which tries to bring the body back to its equilibrium point, giving rise to oscillations or vibrations.
Definition: If a particle that executes periodic motion moves to and fro along the same path. the motion is called oscillation or vibration.
Simple pendulum: A pendulum is suspended from a rigid Support. Let P be the point of suspension and O be the mean or equilibrium position of the bob [Fig.(a)]. If the bob is pulled to the position B and then released, it oscillates along the path BOC. If the angular displacement, i.e., ∠OPB or ∠OPC is less than 4°, then the path BOC or COB may be taken as a straight line. The pendulum is then called a simple pendulum and its oscillation is a linear periodic motion.
Elastic spring: The tipper end of an elastic spring is attached with a rigid support [Fig.(b)]. Let P be the point of suspension. If a heavy body is suspended from its lower end, the spring stretches and the body hangs at rest, at some position of equilibrium O. If the body is slightly pulled to B and then released, the spring executes an up and down oscillatory motion along the straight path BOC and COB. The oscillation of the elastic spring is therefore a linear periodic motion.
Stretched string: A string XY is attached to two rigid supports at points X and Y [Fig.(c)]. It remains at a position of equilibrium along the straight line XY. If the string is pulled slightly upwards or downwards and then released, it vibrates about its position of equilibrium. If we consider a point O on the string, it is seen that the point vibrates along the straight path BOC. This vibration is also a linear periodic motion.
Although any kind of oscillation or vibration is a periodic motion, the converse is not true. All periodic motions are not oscillations or vibrations.
For example, the earth completes one revolution around the sun in 1 year, but it is not a to and 1ro motion about any mean position. Hence the motion is periodic but not oscillatory.
Some Quantities Related to Oscillation
It is evident from the different examples of oscillation above that the motion of the particle is restricted to a line segment, say BC [Fig.].
Complete oscillation: If a vibrating particle starts its motion from any point on its path towards a certain direction, returns to the same point and then follows the same path in the same direction then it is said to have executed one complete oscillation or one complete vibration.
In Fig., if the particle starts its motion from B and after tracing the paths HOC and COB returns to B, then the particle executes one complete oscillation. It is seen that for a complete oscillation, the particle moves along the entire straight path twice. So, if the particle starts its motion from D and after tracing the paths DOC, COB and BD, finally returns to D, then also it can be said that the particle has executed one complete oscillation. A complete oscillation is also known as a period.
Time period: Time period of oscillation of a vibrating particle is defined as the time taken by it to execute one complete oscillation. Its dimension is T and its unit in all systems is second (s).
Frequency: Frequency of oscillation of a vibrating particle is defined as the number of complete oscillations executed by it in 1 second.
In time T, the particle executes one complete oscillation. Thus the number of complete oscillations executed by the particle in 1 s is \(\frac{1}{T}\). Hence, the frequency n of the particle is n = \(\frac{1}{T}\).
Dimension of frequency is T-1 and its unit in all systems is second or per second. This unit of frequency is called hertz (Hz). So, 1 Hz = 1 s-1.
Amplitude: Amplitude of oscillation of a vibrating particle is defined as Its maximum displacement from its equilibrium position.
In Fig., amplitude, A = OB or OC. Dimension of amplitude is L and its units in CGS system and SI are centimetre (cm) and metre (m) respectively.
It is to be noted that in the above discussions, sometimes we have used the term ‘oscillation’ and sometimes ‘vibration’ in fact, oscillation and vibration are synonymous. Usually, when the time period of the particle is large, i.e., frequency is low, the motion of the particle is called oscillation.
Example—oscillation of a simple pendulum or an elastic spring. On the other hand, when the time period of the particle is small, i.e., frequency is high, the motion of the particle is called vibration. Examples of vibration are the vibration of a stretched string or that of a tuning fork.