1. Elasticity and Simple Harmonic Motion Dewi Muliyati Department of Physics State University of Jakarta

2. Outline… Stress, Strain, and Modulus of Elasticity Hooke’s Law Force Constant of Elastic Objects Restoring Force Equation for Displacement in SHM Period of SHM Hooke’s Law for Spring Arrangement Several Benefits of Springs

3. !!! Elasticity is the ability of an object to return to its original shape as soon as the external force which is applied to the object is eliminated (relieved).

4. Stress, Strain, and Modulus of Elasticity Course-1

5. A Pulling Stress, σ Is defined as the quotient between the pulling force F experienced by the wire and its cross-sectional area (A).

6. Strain, e Is defined as the quotient between the change in length ∆L and its initial length L.

7. Stress-Strain Graph

8. Modulus of Elasticity, E The modulus of elasticity, E of a material is defined as the stress-strain ratio experienced by the material.

9. Table: Modulus of Elasticity of Various Substances

10. Hooke’s Law Course-1

11. Hooke’s Law If the pulling force does not exceed the spring’s elastic limit, then the spring’s length increase is directly proportional to the pulling force.

12. Force Constant of Elastic Objects Course-1

13. Force Constant of Elastic Objects E is the modulus of elasticity of material (N/m2) L is the length of object, no force applied (m) A is the cross-sectional area (m2)

14. Restoring Force Course-2

15. Restoring Force The force whose magnitude is proportional to displacement and always acts in the opposite direction of displacement (position). The restoring force always causes an object to move back and forth about the equilibrium point (simple harmonic motion). The restoring force is always opposite to the displacement direction (motion) of the object.

16. Equation for Displacement in SHM Course-2

17. Equation for Displacement in SHM Displacement equation θ0 , the initial phase angle is obtained from the initial condition. A is amplitude. ω is angular frequency.

18. Period of SHM Course-2

19. Period of SHM Acceleration of SHM, Angular Frequency, Period,

20. Hooke’s Law for Spring Arrangement Course-2

21. Serial spring arrangement For the special case of two springs with constants k1 and k2,the spring constant of replacement spring, ks:

22. Parallel spring arrangement For n identical springs in a parallel arrangement, where every spring has a force constant k, the replacement spring constant kp:

23. Several Benefits of Springs Course-2

24. Suspension systems in Motor Vehicles to Damped Shocks

25. Springs on steering wheels