偏微分方程里的问题A uniform string of length πl is fastened at its ends x=0,x=πl.The point x=1/3πl is drawn aside a small distance b ,and the string released from rest at time t=0.Show that,if Tis the tension and ρ the density per unit l

来源:学生作业帮助网 编辑:作业帮 时间:2024/10/04 16:09:32
偏微分方程里的问题A uniform string of length πl is fastened at its ends x=0,x=πl.The point x=1/3πl is drawn aside a small distance b ,and the string released from rest at time t=0.Show that,if Tis the tension and ρ the density per unit l
xRN0Rƕ2S9Zr໨f$121ug_pn;0t{wr֎7jsw}>l_wϫ)tT7݌氾`*.ABЮD2A2c5q0JRP$ ʕ@yjQ )5LgftETʦ4,£=TF.>E`'6Bb/:͖RkT1aKgu"OI̓P饂mezDCL^g2aT$"l~@ dp

偏微分方程里的问题A uniform string of length πl is fastened at its ends x=0,x=πl.The point x=1/3πl is drawn aside a small distance b ,and the string released from rest at time t=0.Show that,if Tis the tension and ρ the density per unit l
偏微分方程里的问题
A uniform string of length πl is fastened at its ends x=0,x=πl.The point x=1/3πl is drawn aside a small distance b ,and the string released from rest at time t=0.Show that,if Tis the tension and ρ the density per unit length of string,the subsequent displacement of the string is

偏微分方程里的问题A uniform string of length πl is fastened at its ends x=0,x=πl.The point x=1/3πl is drawn aside a small distance b ,and the string released from rest at time t=0.Show that,if Tis the tension and ρ the density per unit l
u_tt=a^2u_xx,a^2=T/ρ
u(0,t)=u(πl,0)=0
u(x,0)=f(x)=f_1(x)=3bx/(πl),0