An expression which can be used to evaluate the relative error in g (in terms of h, Δh, t, and Δt) is: [tex]\delta = \frac{t^2(h\;+\Delta \;h) }{h(t\;+\;\Delta t)^2} - 1[/tex]
Relative error can be defined as a measure of the ratio of an absolute (real) value of a measurement to an expected (theoretical) value. Also, it's independent of the magnitude of its values.
In order to write this expression, we would divide the absolute (real) value by the expected (theoretical) value as follows:
[tex]\delta = \frac{g(h\;+\;\Delta h,t \;+ \;\Delta t) - \;g(h,t)}{g(h,t)} \\\\\delta = \frac{g(h\;+\;\Delta h,t \;+ \;\Delta t) }{g(h,t)} - 1\\\\\delta = \frac{t^2(h\;+\Delta \;h) }{h(t\;+\;\Delta t)^2} - 1[/tex]
Note: g = 2h/t²
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