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
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![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](/uploads/image/z/10371306-66-6.jpg?t=%E5%81%8F%E5%BE%AE%E5%88%86%E6%96%B9%E7%A8%8B%E9%87%8C%E7%9A%84%E9%97%AE%E9%A2%98A+uniform+string+of+length+%CF%80l+is+fastened+at+its+ends+x%3D0%2Cx%3D%CF%80l.The+point+x%3D1%2F3%CF%80l+is+drawn+aside+a+small+distance+b+%2Cand+the+string+released+from+rest+at+time+t%3D0.Show+that%2Cif+Tis+the+tension+and+%CF%81+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 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