Let $u(x, t)$ denote the displacement of a point on a rod. The displacement satisfies the following equation of motion: $\frac{\partial^{2} u}{\partial t^{2}}-25 \frac{\partial^{2} u}{\partial x^{2}}=0, \quad 0<x<1$ with $u(x, 0)=0.01 \sin (10 \pi x), \frac{\partial u}{\partial t}(x, 0)=0 ; u(0, t)=0, u(1, t)=0 .$ The value of $u(0.25,1)$
is ______________$\quad$ (in three decimal places).

Question ID - 155578 | SaraNextGen Top Answer

Let $u(x, t)$ denote the displacement of a point on a rod. The displacement satisfies the following equation of motion: $\frac{\partial^{2} u}{\partial t^{2}}-25 \frac{\partial^{2} u}{\partial x^{2}}=0, \quad 0<x<1$ with $u(x, 0)=0.01 \sin (10 \pi x), \frac{\partial u}{\partial t}(x, 0)=0 ; u(0, t)=0, u(1, t)=0 .$ The value of $u(0.25,1)$
is ______________$\quad$ (in three decimal places).