1. Transient

2. Equation of motion resistance force is proportional to speed : For convenience: Also, k=m  0 2 Trial solution

3. Underdamped Two solutions with

5. The real solution of equation of motion

6. Damped cosine oscillation

7. Logarithmic decrement A1A1 A2A2 A3A3 A4A4

8. Phase difference between x and v is not simply  /2.

9. To find E and F we choose the initial conditions with

10. High Damping

12. For very high damping

13. © SB For very high damping

14. Two different time scale involved in damped SHM

15. Critical Damping General Solution

17. Transient : Damped oscillation with no forcing Use the link: http://www.walter-fendt.de/ph14e/resonance.htm © Walter Fendt

18. PROBLEM A door shutter has a spring which, in the absence of damping, shuts the door in 0.5 seconds. The problem is that the door bangs shut with a speed 1 m/s. A damper with a damping coefficient  is introduced to ensure that the door shuts gradually. What is the time required for the door to shut and the velocity at the instant it shuts, if  = 0. 5 . Note that the spring is unstretched when the door is shut.

19. Transients Equation of motion For low damping

20. For high damping For critical damping

21. FEYNMAN LECTURES ON PHYSICS VOL I Author : RICHARD P FEYNMAN, IIT KGP Central Library : Class no. 530.4