1. I.II Equation of motion i- Characteristics of a SDOF Why SDOF?
1- Simple starting point
2- Many multi-degree of freedom structures can be approximated by a SDOF system
i- Characteristics of a SDOF
1- Rigid girder of mass m ()
2- Weightless columns of stiffness k
3- Weightless a damper with a damping coefficient c

2. ii- Newton’s second law
FI = rate of change of momentum of any mass is equal to the force acting on it
(for constant m)
iii- D’Alembert principle (dynamic equilibrium)

3. Where

4. Example 1[Ref 1 ] Weight = w lb Length = 10’ E = 29,000 ksi
and
The weight contribution !!

5. Example 1 (cont’d)

6. Example 2 [Ref 1 ]