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# Elasticity and Simple Harmonic Motion

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### Elasticity and Simple Harmonic Motion

1. 1. Elasticity and Simple Harmonic Motion<br />Dewi Muliyati<br />Department of Physics <br />State University of Jakarta<br />
2. 2. Outline…<br />Stress, Strain, and Modulus of Elasticity<br />Hooke’s Law<br />Force Constant of Elastic Objects<br />Restoring Force<br />Equation for Displacement in SHM<br />Period of SHM<br />Hooke’s Law for Spring Arrangement<br />Several Benefits of Springs<br />
3. 3. !!!<br />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).<br />
4. 4. Stress, Strain, and Modulus of Elasticity<br />Course-1<br />
5. 5. A Pulling Stress, σ<br />Is defined as the quotient between the pulling force F experienced by the wire and its cross-sectional area (A).<br />
6. 6. Strain, e<br />Is defined as the quotient between the change in length ∆L and its initial length L.<br />
7. 7. Stress-Strain Graph<br />
8. 8. Modulus of Elasticity, E<br />The modulus of elasticity, E of a material is defined as the stress-strain ratio experienced by the material.<br />
9. 9. Table: Modulus of Elasticity of Various Substances<br />
10. 10. Hooke’s Law<br />Course-1<br />
11. 11. Hooke’s Law<br />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.<br />
12. 12. Force Constant of Elastic Objects<br />Course-1<br />
13. 13. Force Constant of Elastic Objects<br />E is the modulus of elasticity of material (N/m2)<br />L is the length of object, no force applied (m)<br />A is the cross-sectional area (m2)<br />
14. 14. Restoring Force<br />Course-2<br />
15. 15. Restoring Force<br />The force whose magnitude is proportional to displacement and always acts in the opposite direction of displacement (position).<br />The restoring force always causes an object to move back and forth about the equilibrium point (simple harmonic motion).<br />The restoring force is always opposite to the displacement direction (motion) of the object.<br />
16. 16. Equation for Displacement in SHM<br />Course-2<br />
17. 17. Equation for Displacement in SHM<br />Displacement equation<br />θ0 , the initial phase angle is obtained from the initial condition.<br />A is amplitude.<br />ω is angular frequency.<br />
18. 18. Period of SHM<br />Course-2<br />
19. 19. Period of SHM<br />Acceleration of SHM,<br />Angular Frequency,<br />Period,<br />
20. 20. Hooke’s Law for Spring Arrangement<br />Course-2<br />
21. 21. Serial spring arrangement<br />For the special case of two springs with constants k1 and k2,the spring constant of replacement spring, ks:<br />
22. 22. Parallel spring arrangement<br />For n identical springs in a parallel arrangement, where every spring has a force constant k, the replacement spring constant kp:<br />
23. 23. Several Benefits of Springs<br />Course-2<br />
24. 24. Suspension systems in Motor Vehicles to Damped Shocks<br />
25. 25. Springs on steering wheels<br />