Part I – Basics (1) Geometric model: - interconnected model elements (2) DOFs of a geometric model (3) FBDs of model elements (4) Elemental equations (5) Energy storage and dissipation (6) Obtain model parameters (7) Obtain simplified equivalent systems hw1~hw4. Also, examples in notes.

Part II – SDOF systems 2.1 Free vibration of undamped system (1) Obtain math model (hw4) 𝑎 2 𝑦 + 𝑎 𝑜 𝑦=0 (2) Solution for the vibration (hw5) (3) System property and application (hw5) - the natural frequency: Examples in notes.

2.2 Free vibration of damped system (1) Obtain math model (hw6) 𝑎 2 𝑦 + 𝑎 1 𝑦 + 𝑎 𝑜 𝑦=0 or 𝑦 +2𝜉 𝜔 𝑛 𝑦 + 𝜔 𝑛 2 𝑦=0 𝜔 𝑛 = 𝑎 𝑜 / 𝑎 2 and 𝜉= 1 2 𝜔 𝑛 𝑎 1 𝑎 2 (2) Solution for the vibration (hw7) underdamped: 𝑦 𝑡 =𝐴 𝑒 −𝜉 𝜔 𝑛 𝑡 sin( 𝜔 𝑑 𝑡+𝜙) critically damped: 𝑦 𝑡 = (𝐴 1 + 𝐴 2 𝑡) 𝑒 − 𝜔 𝑛 𝑡 overdamped: 𝑦 𝑡 = 𝐴 1 𝑒 𝑠 1 𝑡 + 𝐴 2 𝑒 𝑠 2 𝑡 (3) System property and application (hw7) For underdamped systems: 𝜔 𝑛 , 𝜉 ~( 𝑇 𝑑 , 𝛿) relations

2.3 Harmonically excited vibration (1) Obtain math model (hw8) 𝑎 2 𝑦 + 𝑎 1 𝑦 + 𝑎 𝑜 𝑦=ℎ(𝑡) or 𝑦 +2𝜉 𝜔 𝑛 𝑦 + 𝜔 𝑛 2 𝑦=𝐸𝑠𝑖𝑛𝜔𝑡 (2) Solution for the vibration (hw8) 𝑦 𝑡 = 𝑦 ℎ 𝑡 + 𝑦 𝑝 (𝑡) 𝑦 ℎ (𝑡) same expression as 𝑦(𝑡) in 2.2, different 𝐴 1 , 𝐴 2 𝑦 𝑝 𝑡 =𝑌𝑠𝑖𝑛(𝜔𝑡+𝜓) Y by Eq. (M): 𝑌= 𝐸/ 𝜔 𝑛 2 (1− 𝑟 2 ) 2 + (2𝜉𝑟) 2 1/2 𝜓 by Eq. (P): 𝜓=− 𝑡𝑎𝑛 2 −1 2𝜉𝑟 1− 𝑟 2 (3) Application (hw9) 𝑌,𝜓 ~ 𝐸, 𝜔 ~( 𝜔 𝑛 , 𝜉) relations