Periodic and Simple Harmonic Oscillation.pptx

It provides basic idea about motion and its type. In addition to that you can understand what is SHM and it equation

1. The motion is the change in position of an object with respect to its surroundings in a given interval of time. Motion is always observed and measured with a point of reference All living things show motion whereas non living things shows motion only when some force acting on it What is Motion? Introduction

2. Types of Motion

3. Oscillatory motion can be termed as the repeated motion in which an object repeats the same movement over and over. In the absence of friction, the oscillatory motion would continue forever; but in the real world, the system eventually settles into equilibrium. A motion occurs even at atomic levels can be said to be Oscillatory. When the temperature is raised, the atoms in a solid vibrate about their rest position (mean position or equilibrium position).

4. RC oscillator is used to generate a Low Frequency signal LC oscillator is used to generate a High Frequency signal Op-Amp based oscillator is used to generate a stable frequency . For example The study of vibrational motion is very important in Electronics and Communication Engineering applications to study and generate a signal.

5. What is Periodic Motion? Motion which repeat itself after a regular interval of time is known as Periodic motion Periodic Motion a bouncing ball a vibrating tuning fork a swing in motion the Earth in its orbit around the Sun, and a water wave.

6. What is Non Periodic Motion? Motion which does not repeat itself after a regular interval of time is known as non-periodic motion. Non Periodic Motion Example : Occurrence of Earth quake eruption of volcano

7. When an object or a particle moves back and forth repeatedly for some duration of time its motion is said to be oscillatory or vibratory. All oscillatory motions are periodic whereas all periodic motions need not be oscillation in nature. Oscillatory Motion

8. Free oscillations Damped oscillations Maintained oscillations Forced oscillations Resonance Types of oscillations

9. When the oscillator is allowed to oscillate by displacing its position from equilibrium position (or mean position), it oscillates with a frequency which is equal to the natural frequency of the oscillator. Such an oscillation or vibration is known as free oscillation or free vibration. Free oscillations

10. In reality, in a medium, due to the presence of friction and air drag, the amplitude of oscillation decreases as time progresses. It implies that the oscillation is not sustained and the energy of the SHM decreases gradually indicating the loss of energy. The energy lost is absorbed by the surrounding medium. This type of oscillatory motion is known as damped oscillation. Damped oscillations

11. By supplying energy from an external source, the amplitude of the oscillation can be made constant. Such vibrations are known as maintained vibrations. Maintained oscillations

12. Any oscillator driven by an external periodic agency to overcome the damping is known as forced oscillator or driven oscillator. In this type of vibration, the body executing vibration initially vibrates with its natural frequency and due to the presence of external periodic force, the body later vibrates with the frequency of the applied periodic force. Such vibrations are known as forced vibrations. Forced oscillations

13. It is a special case of forced vibrations where the frequency of external periodic force (or driving force) matches with the natural frequency of the vibrating body (driven). As a result the oscillating body begins to vibrate such that its amplitude increases at each step and ultimately it has a large amplitude. Such a phenomenon is known as resonance and the corresponding vibrations are known as resonance vibrations. Resonance

14. Oscillation or Vibration – a motion that repeats itself with no net displacement. Equilibrium Position – the point that the object oscillates around. Also known as the rest position. Displacement – how far the mass is from the equilibrium point (x) Maximum displacement – how far the mass moves from the equilibrium position. (x max occurs at A) TERMINOLOGY

15. TERMINOLOGY Amplitude (A) – the distance from the equilibrium point to the maximum displacement. Cycle – a complete to and fro motion. Period (T) – the time needed to complete one cycle. (Unit – Seconds) Frequency (f) – the number of cycles completed in one second. (Unit – Hertz) Formula f=1/T T=1/f

16. Any vibrating system where the restoring force is proportional to the negative of the displacement is called simple harmonic motion (SHM) and is often called a simple harmonic oscillator (SHO). Simple Harmonic Motion

17. If an object vibrates or oscillates back and forth over the same path, each cycle taking the same amount of time, the motion is called periodic. The mass and spring system is a useful model for a SHM system. Oscillations of a Spring

18. We assume that the surface is frictionless. There is a point where the spring is neither stretched nor compressed; this is the equilibrium position. We measure displacement from that point ( x = 0 on the previous figure). The force exerted by the spring depends on the displacement: Oscillations of a Spring

19. The minus sign on the force indicates that it is a restoring force—it is directed to restore the mass to its equilibrium position. k is the spring constant. The force is not constant, so the acceleration is not constant either. Oscillations of a Spring

20. Oscillations of a Spring

21. Substituting F = kx into Newton’s second law gives the equation of motion: with solutions of the form : Simple Harmonic Motion

22. Substituting, we verify that this solution does indeed satisfy the equation of motion, with: The constants A and φ will be determined by initial conditions; A is the amplitude, and φ gives the phase of the motion at t = 0. Simple Harmonic Motion