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Periodic motion occurs when a body recurs its motion along a specific path, about a given point after a certain period of time.
- The period of motion is the fixed interval of time after which the motion is repeated.
- The necessary condition for a body or object's motion to be periodic is that it has a distinct period where the shortest interval of time after which the periodic motion of a body repeats itself is known as the period T.
- A girl swinging on a swing, a sewing machine needle, a clock's pendulum, Guitar strings, etc. are examples of periodic motion.
Simple Harmonic Motion (SHM) is a common widely studied type of periodic motion.
- In an ideal system (a system with no resistive force to the moving object), the object that moves in the system derives restoring force, allowing the system to oscillate from the extreme point on one end to the equilibrium position and then to the other extreme end indefinitely.
- In ideal conditions, there is no damping effect on the motion.
- The mass-spring oscillator, the oscillating pendulum, uniform circular motion, oscillatory motion, and so on are all examples of simple harmonic motion.
Very Short Answers Questions [1 Mark Questions]
Ques. A person goes to bed at sharp 10.00 pm every day. Is it an example of periodic motion? If yes, what is the time period? If not, why?
Ans. No, because motion is defined as a change in the position of an object with respect to time or a reference point, it is not an example of periodic motion.
Ques. What is meant by motion?
Ans. A body is said to be in motion when its position or orientation varies with respect to time and surroundings.
Ques. What is meant by periodic motion?
Ans. In physics, periodic motion is defined as motion that occurs at equal time intervals. A rocking rocker, a bouncing ball, a vibrating tuning fork, a swing in motion, the Earth in its orbit around the Sun, and a water wave are all examples of periodic motion.
Ques. What is circular motion?
Ans. A circular motion is the movement of an object around the perimeter of a circle or the rotation of an object around a circular arc. It might be uniform (constant rate of rotation and tangential speed) or non-uniform (varying rate of rotation).
Ques. A motion can be periodic and not oscillatory.
- True
- False
Ans. The correct answer is a. True
Explanation: A motion can be periodic and not oscillatory. Uniform circular motion, for example, is periodic but not oscillatory.
Ques. A simple pendulum of length l and with a bob whose mass is m is moving along a circular arc of angle θ in a vertical plane. A sphere of mass m is placed at the end of the circle. What momentum will be given to the sphere by the moving bob?
- Constant
- Zero
- Unity
- Infinity
Ans. The correct answer is b. Zero
Explanation: The momentum imparted to the sphere by the moving bob is 0 since the bob's velocity at the end of the arc is zero.
Short Answers Questions [2 Marks Questions]
Ques. How is time measured using periodic motion?
Ans. We can use periodic motion to measure time if we know the period of the motion, which is the time it takes for the motion to complete one cycle. After that, we may count the periods and multiply the counted value by the period value to get the time in seconds.
Ques. Are all periodic motions oscillatory? Explain.
Ans. No, not all oscillatory periodic motions are oscillatory. An object in periodic motion repeats its motion at regular intervals of time, although the path may or may not be "to and fro" (oscillatory).
A man jogging on a circular track at a constant speed, for example, exhibits periodic motion but not oscillatory motion.
Ques. Give some examples that have both periodic motion and simple harmonic motion.
Ans. A vibrating tuning fork, the Earth revolving around the Sun, a swing in motion, a water wave, and a functioning pendulum are all examples of periodic motions. Simple harmonic motion is a subset of periodic motion. Simple harmonic motion are performed by a water wave, a swing, and a tuning fork. The Earth's revolution, on the other hand, and the bouncing ball are not subject to the principles of harmonic motion.
Ques. What is the relationship between simple harmonic motion and periodic motion?
Ans. Any type of repeating motion is referred to as periodic motion. Whereas simple harmonic motion is a type of periodic motion in which the restoring force is proportional to the displacement.
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Long Answers Questions [3 Marks Questions]
Ques. Give a brief about the connection between a pendulum and periodic motion.
Ans. The connection between a pendulum and periodic motion is given below
- Swinging a weight on a string causes it to move back and forth in a constant periodic pattern.
- If there is no air resistance and internal friction in the supporting thread, a pendulum will travel back and forth indefinitely after it begins its motion.
- The gravitational force causes the pendulum weight to swing in different directions, while the pull from the string causes it to move in a semi-circular motion.
Ques. Give two examples for each of the following motions :
- Linear motion
- Oscillatory motion
- Spinning motion
- Periodic motion
- Circular motion
- Vibrational motion
- Random motion
Ans. The examples of the mentioned types of motion are
- Linear motion: Rolling of the ball, Moving of bicycle on the road
- Oscillatory motion: Pendulum of clock, Motion of a child on a swing
- Spinning motion: Rotating fan, Wheel of sewing machine
- Periodic motion: Pendulum of clock, Motion of a swing, heartbeat
- Circular motion: Rotation of fan, Bicycle wheel
- Vibrational motion: String of a guitar, Surface of drums
- Random motion: Motion of football players, Movement of mosquito.
Ques. Every periodic motion is a uniform motion. Explain.
Ans. A periodic motion is one that repeats itself after a regular interval of time, whereas a uniform motion is one in which an object covers the same distance in regular successive periods of time.
- Because the motion is repeated in regular intervals of time, the object covers the same distance in those regular intervals of time as in periodic motion.
- As a result, we can say that the object is also moving uniformly.
- However, not all uniform motions are periodic since they may or may not follow the same path repeatedly.
Very Long Answers Questions [5 Marks Questions]
Ques. Give a brief about the connection between a bouncing ball and periodic motion.
Ans. The connection between a bouncing ball and periodic motion is given below
- The gravitational force pulls a rubber ball back towards the Earth's surface when it is thrown upward.
- When it hits the surface, the force of the impact changes the direction of the velocity of the ball, and it moves upward, traveling up and down in a periodic or regular manner.
- An ideal rubber ball will keep bouncing for a long time.
- The ball jumps less and less with each successive bounce due to air resistance and internal friction until it eventually stops.
- An ideal rubber ball may bounce indefinitely (in an environment with no outside factors to slow it down).
Ques. What are the characteristics of periodic motion?
Ans. The velocity of the object, the period of motion, and the amplitude of the motion are all characteristics of periodic motion.
- Periodic motion may be observed in many waveforms and is employed in clocks and other devices.
- Time period refers to the amount of time it takes a particle with periodic motion to pass a certain place from a specific direction at regular intervals.
- A periodic motion's path might be circular, elliptical, linear, or more complicated.
Periodic motion has three similar characteristics:
- Velocity: All bodies in periodic motion must have velocity, which is defined as the rate of change of displacement with time. It is represented by the symbol v.
- Period: The time it takes an object to move back and forth around its mean position is referred to as the time period and is indicated by the symbol T.
- Amplitude: The maximum displacement of an object from its mean position is defined as its amplitude.
Ques. Every SHM is a periodic motion. But all periodic motions are not SHM why? Explain with an example
Ans. Any type of repetitive motion is considered a periodic motion.
- A simple harmonic motion occurs when an object travels to and fro around a mean position, and the restoring force on the moving object is proportional to its displacement in either direction.
- The speed of a moving object in SHM is zero at extreme positions and maximum at the mean position.
- As in a pendulum, the bob stops at the extreme positions (zero speed) and reaches a maximum speed at the mean position (bob's bottommost position).
- All other periodic motions that do not meet this requirement are not simple harmonic.
- For example, the earth revolves around the sun, a fan rotates uniformly, and so on.
- The angular speed of the earth or a fan is constant, not zero or maximum at any point.
- Also, the earth or a fan do not move back and forth; they only move in one direction.
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