Derive the equation of motion for the string?

from a microscopic model. Assume a simple model of a string as a set of masses ?m spaced evenly on the x axis at regular intervals of ?x, connected by springs of spring constant k = ?/?x. Compute the leading term in the force on each mass and take the limit ?x ? 0 to get the string wave equation, where ? = ?m/?x. In the same limit show that the energy density of the string is given by eq.?

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a2 a,2 y(x, 1) = t (x, t) a2