In physics, a periodic motion is a type of motion which is repeated in equal time intervals. Some of the familiar periodic motions are a vibrating tuning fork, the Earth revolving around the Sun, a swing in motion, a water wave, and a working pendulum. Take the case of a normal pendulum; if weight is swung on a string, it will move back and forth in steady periodic motion. When it starts this motion, a pendulum will move back and forth endlessly if there is no air resistance and internal friction in the supporting string. The gravitational force pushes the pendulum’s weight to vary in direction while the force arising from the string displaces it in a semi-circular motion. In the case of a bouncing ball, when a rubber ball is thrown, the gravitational force pulls it back towards the Earth’s surface. When it strikes the surface, the force of the collision varies the direction of velocity, and the ball travels upward, moving up and down in a periodic or regular manner. An ideal rubber ball will stay bouncing for a long period of time. Due to the air resistance and internal friction, the ball jumps less and less after each succeeding bounce until it eventually stops.
In every case, the time interval for the cycle or repetition of the motion is known as a period, while the frequency is the number of periods per unit time. Therefore, the period of the revolution of the Earth is one year (365 Earth days), and one orbit per year is the frequency. Interestingly, simple harmonic motion is a distinct instance of periodic motion. From the above examples, the water wave, the swing and the tuning fork perform simple harmonic motions. On the other hand, the revolution of the Earth and the bouncing ball do not follow the principles of harmonic motion. Waves that can be denoted by sine curves are always periodic. If waves are travelling with a wavelength λ and a velocity v, then the value of period T is equivalent to the given wavelength divided by velocity (T = λ/v). We also know that frequency f is exactly reciprocal to the period of the wave; therefore, f = 1/T = v/λ.
Periodic Motion Questions and Answers
1) What is meant by periodic motion?
A periodic motion is a type of motion which is repeated in equal time intervals. Some of the familiar periodic motions are a vibrating tuning fork, the Earth revolving around the Sun, a swing in motion, a water wave, and a working pendulum.
2) What is circular motion?
Movement of an object while rotating along a circular path is known as circular motion.
3) Give some examples that have both periodic motion and simple harmonic motion.
Some of the familiar periodic motions are a vibrating tuning fork, the Earth revolving around the Sun, a swing in motion, a water wave, and a working pendulum. Simple harmonic motion is a distinct instance of periodic motion. A water wave, the swing and the tuning fork perform simple harmonic motions. On the other hand, the revolution of the Earth and the bouncing ball do not follow the principles of harmonic motion.
4) What is meant by time period (T)?
The time period is the time required by a movement to repeat itself. Therefore, the measuring unit of the time period is in seconds.
5) What is meant by frequency (f)?
The frequency (f) is the cycle of motion repeated in one unit time (seconds). Hertz (Hz) is the basic unit of frequency.
The frequency is given by the equation, f = 1/T.
Where,
f = frequency
T = Time Period
6) What is meant by displacement?
It is the distance of the object from its mean (rest) position at a given time. It is measured in cm, mm, etc.
7) What is meant by the amplitude?
It is the maximum displacement covered by the oscillator from either side of its (mean) rest position.
8) What is meant by phase (φ)?
The phase is the angle whose cosine or sine at a given time shows the direction and position of the oscillator’s motion. It is represented in radians.
9) What is meant by angular frequency (ω)?
Angular frequency is equal to phase angle change per unit time. It is represented in rad per second.
10) Give a brief about the connection between a bouncing ball and periodic motion.
When a rubber ball is thrown, the gravitational force pulls it back towards the Earth’s surface. When it strikes the surface, the force of the collision varies the velocity’s direction, and the ball travels upward, moving up and down in a periodic or regular manner. An ideal rubber ball will stay bouncing for a long period of time. Due to the air resistance and internal friction, the ball jumps less and less after each succeeding bounce until it eventually stops. An ideal rubber ball could bounce periodically forever (in an environment without any external constraints to slow it down).
11) Give a brief about the connection between a pendulum and periodic motion.
If weight is swung on a string, it will move back and forth in steady periodic motion. When it starts this motion, a pendulum will move back and forth endlessly if there is no air resistance and internal friction in the supporting string. The gravitational force forces the pendulum weight to vary in direction while the force arising from the string displaces it in a semi-circular motion.
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Practice Questions
1) What is meant by motion?
2) What is the relationship between simple harmonic motion and periodic motion?
3) What is the main difference between horizontal and vertical motion?
4) What are the applications of periodic motion?
5) What is the relationship between friction and periodic motion?
6) What is the principle behind the working of a pendulum?
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