2. Simple Harmonic Motion

3. Oscillatory Systems §Periodic motion §Elasticity §Inertia §Interchange of energies §Examples: l Mass on helical spring l Cantilever l Simple pendulum l Vertical rod floating in liquid

4. Characteristics of SHM §Occurs in many systems §Isochronous oscillation §Possesses springiness (elasticity) to store P.E. §Possesses inertia to store K.E. §Period of vibration depends on elastic and inertia factors §Constant total energy

5. §Conditions for performing SHM l acceleration is always directed towards a fixed point l acceleration varies directly as its distance from the fixed point l i.e. in linear motion in angular motion

6. Figures

7. Terms of Reference §Amplitude §Period §Frequency l unit: Hertz

8. Rotating Vector Model §As particle N describes uniform circular motion, its projection point P performs simple harmonic motion §computer simulationcomputer simulation

9. Kinematics of SHM §Displacement: x = a cos  t §Velocity: §Acceleration:

10. Graphs of SHM

11. General Relation between x & t Where  is the phase angle

12. Experimental Verification of the relationship Experimental set up:

13. § Procedure: §Displacement-time graph Experimental Verification of the relationship

14. x-t and graphs

15. Graph x

16. Solving Problems on SHM §Assume displacement x from the mean position §Draw a diagram showing all forces §Apply Newton’s second law with appropriate sign convention §Show that §The constant of proportionality =  2 §Period T = 2  / 

17. Mass on a Spiral Spring §Motion on a smooth horizontal surface

18. Graph

19. §Motion under gravity

20. Floating Tube in a Liquid (1)

21. Floating Tube in a Liquid (2) Effects of viscosity of liquid: causes damping takes away K.E. from the oscillating tube

22. Liquid Oscillating in a U-tube

23. Simple Pendulum

24. Arrangement of Springs (1) K = equivalent spring constant

25. § Springs connected in series: Arrangement of Springs (2)

26. § Springs connected in parallel: Arrangement of Springs (3)

27. Energy in SHM (1)

28. Energy in SHM (2)

29. Phase Difference § Phase leading § Phase lagging § In phase § Out of phase (Antiphase)

30. Superposition of Two Harmonic Variations §The amplitude and phase of the resultant is obtained by the parallelogram law

31. Experimental Determination of g (1) §a) A simple pendulum: Plot a graph of T 2 vs l Slope =

32. §b) A loaded spring: i) The static experiment: Plot the extension-load graph Slope: Experimental Determination of g (2)

33. Experimental Determination of g (3) ii) The dynamic experiment: measure the period of oscillation for different loads

34. EXAMPLES