One-dimensional wave equation

A vibrating string with a second time derivative, so separation gives standing modes that oscillate rather than decay, superposed to match a plucked initial shape.

Notes on Diffy Qs: Differential Equations for Engineers, One-dimensional wave equation

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4 exercises

Exercise 101

Solve

2.5

Exercise 102

Solve

2.5

Exercise 103

Solve

2.5

Exercise 104

What happens when $a=0$ ? Find a solution to $y_{tt} = 0$ , $y(0,t) = y(\pi,t) = 0$ , $y(x,0) = \sin(2x)$ , $y_t(x,0) = \sin(x)$ .

2.5