弦的横振动方程 02u (T sin 0)x+dr-Tsin 0)x=dm (T cos 0)x+dr-(T cos 0)2=0 sinb≈tan0= cosb≈1
Equations of Mathematical Physics Boundary & Initial Conditions PDE’s Well-posed Problem Transverse Vibration of Strings Longitudinal Vibration of Flexible Rods Heat Conduction Equation Time-independent and Steady-state Problems uîħ (T sin θ)x+dx − (T sin θ)x = dm ∂ 2u ∂t2 (T cos θ)x+dx − (T cos θ)x = 0 ∂u ∂x 1 =⇒ sin θ ≈ tan θ = ∂u ∂x cos θ ≈ 1 C. S. Wu 18ù êÆÔn§
弦的横振动方程 02u (T sin 0)x+dr-Tsin 0)x=dm (T cos 0)x+dr-(T cos 0)2=0 du sin6≈ tan 0 du cosb≈1 cos≈1=()+d-(m)2=0 即T不随x变化,弦中各点张力相等
Equations of Mathematical Physics Boundary & Initial Conditions PDE’s Well-posed Problem Transverse Vibration of Strings Longitudinal Vibration of Flexible Rods Heat Conduction Equation Time-independent and Steady-state Problems uîħ (T sin θ)x+dx − (T sin θ)x = dm ∂ 2u ∂t2 (T cos θ)x+dx − (T cos θ)x = 0 ∂u ∂x 1 =⇒ sin θ ≈ tan θ = ∂u ∂x cos θ ≈ 1 cos θ ≈ 1 =⇒ (T)x+dx − (T)x = 0 =TØxCz§u¥:Üå C. S. Wu 18ù êÆÔn§
弦的横振动方程 02u (T sin 0)x+dr-Tsin 0)x=dm (T cos 0)x+dr-(T cos 0)2=0 du sin6≈ tan 0 du cosb≈1 02u a2 T at2 尜
Equations of Mathematical Physics Boundary & Initial Conditions PDE’s Well-posed Problem Transverse Vibration of Strings Longitudinal Vibration of Flexible Rods Heat Conduction Equation Time-independent and Steady-state Problems uîħ (T sin θ)x+dx − (T sin θ)x = dm ∂ 2u ∂t2 (T cos θ)x+dx − (T cos θ)x = 0 ∂u ∂x 1 =⇒ sin θ ≈ tan θ = ∂u ∂x cos θ ≈ 1 ρdx ∂ 2u ∂t2 = T ∂u ∂x x+dx − ∂u ∂x x = T ∂ 2u ∂x2 dx C. S. Wu 18ù êÆÔn§
lysate Probler 弦的横振动方程 u a2 at2 其中卩是弦的线密度(单位长度的质量).定义 是弦的振动传
Equations of Mathematical Physics Boundary & Initial Conditions PDE’s Well-posed Problem Transverse Vibration of Strings Longitudinal Vibration of Flexible Rods Heat Conduction Equation Time-independent and Steady-state Problems uîħ ρ ∂ 2u ∂t2 − T ∂ 2u ∂x2 = 0 Ù¥ρ´uÝ(ü Ýþ)©½Â a = p T/ρ K§±¤ ∂ 2u ∂t2 − a 2 ∂ 2u ∂x2 = 0 aÒ´uÄDÂÝ C. S. Wu 18ù êÆÔn§
lysate Probler 弦的横振动方程 u a2 at2 其中ρ是弦的线密度(单位长度的质量).定义 则方程可以写成 a就是弦的振动传播速度
Equations of Mathematical Physics Boundary & Initial Conditions PDE’s Well-posed Problem Transverse Vibration of Strings Longitudinal Vibration of Flexible Rods Heat Conduction Equation Time-independent and Steady-state Problems uîħ ρ ∂ 2u ∂t2 − T ∂ 2u ∂x2 = 0 Ù¥ρ´uÝ(ü Ýþ)©½Â a = p T/ρ K§±¤ ∂ 2u ∂t2 − a 2 ∂ 2u ∂x2 = 0 aÒ´uÄDÂÝ C. S. Wu 18ù êÆÔn§