The amount of elastic potential energy (EPE) stored in a string is given by the following equation
Where Δl is the extension resulting from the tensioning of the string and the plucking action, l is the natural length of the string and Qs is the net elasticity or relative strength of the wire
Q = Young's modulus
d = diameter
To calculate the amount of energy stored in a harp string with its known parameters when under tension the natural length l of the string must be established first in order to calculate the elongation Δl.
Δl1 = the elongation resulting from the initial string tension
Δl2 = the elongation resulting from the plucking action
Δl = ??Δl1+Δl2 = total elongation
l = the natural length of the string
l1 = the vibrating length of the string under tension
From Hookes Law
Values for Qs (Q and d), l1 and T are known for any given string, allowing Δl1 to be calculated and therefore l, which is equal to l1-Δl1
The elongation resulting from the plucking action Δl2 can be calculated thus
Where Pp is the plucking point and Pd is the plucking depth.