WAVE AND OSCILLATION - SIMPLE HORMONIC MOTION .pptx

EXPRESSION FOR DISPLACEMENT , VELOCITY , ACCELERATION OF A PARTICLE EXECUTING SHM

1. WAVE AND OSCILLATION SIMPLE HORMONIC MOTION EXPRESSION FOR DISPLACEMENT , VELOCITY , ACCELERATION OF A PARTICLE EXECUTING SHM

2. SIMPLE HARMONIC MOTION If a particle moves in a straight line , so that its acceleration is always directed towards a fixed point on the line , and is proportional to its displacement from the fixed point , the particle is said to move with simple harmonic motion .

3. PERIODIC AND OSCILLATORY MOTIONS OSCILLATORY MOTION W hen an object or a particle executes To and Fro motion repeatedly for some duration of time its motion is said to be oscillatory motion. Example; our heart beat , swing of an wings of an insect , grand father’s clock , etc ,….

4. PERIODIC MOTION Any motion which repeats itself in a fixed time interval is known as periodic motion. PERIODIC AND OSCILLATORY MOTIONS Example; rocking chair, a bouncing ball, a vibrating tuning fork, a swing in motion, the Earth in its orbit around the Sun, and a water wave.

5. EXPRESSION FOR DISPLACEMENT , VELOCITY , ACCELERATION OF A PARTICLE EXECUTING SHM Let ‘P’ be a particle moving on the circumference of a circle of ‘A’ with a uniform angular velocity . ‘O’ is the center of the circle . A perpendicular ‘PK’ is drawn from the particle on the diameter ‘ YY’ ’ of the circle. As the particle ‘P’ moves round the circle , the foot of the perpendicular ‘K’ , vibrates along the diameter ‘ YY’ ’. Since the motion of ‘P’ is uniform , the motion of ‘K’ is periodic .As the particle ‘P’ completes one revolution , the foot of the perpendicular ‘K’ completes one vertical oscillation. The distance ‘OK’ is called the displacement and is denoted by ‘y’  

6. The particle moves from ‘x’ to ‘P’ in time ‘t’. Let, From the ‘OK’ is called the displacement of the vibrating particle.  

7. The displacement of a vibrating particle at any instant can be defined as its distance from the mean position of rest, Displacement , . The change in the displacement of a vibration particle in one completes vibration,  

8. From the diagram, Square and add on both sides, equation of circle.  

9. The velocity of a vibrating particle can be defined as the ratio of the rate of change of displacement by time, Velocity, When y=0; at mean position max  

10. The acceleration of a vibrating particle can be defined as the ratio of the rate of change of velocity by time , Thus, acceleration is directly proportional to displacement and directed towards a fixed point. This type of motion is called Simple Harmonic Motion.  

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