Answer:
a♦1 E_average = n E₀ / 2 , b) E_average= infinity
Explanation:
The energy values form an arithmetic series, whose sum is
S = n (a₁ + aₙ) / 2 = n (2a₁ + (n-1) r)/ 2
Where n is the number of terms, a₁ is the first term, aₙ the last term and r is the difference between two consecutive numbers in the series
r = 2E₀ - 0 = 2E₀
Therefore the sum is
S = n (0 + n E₀) / 2
S = n² E₀ / 2
The average value is
E_average = S / n
E_average = n E₀ / 2
b) the case of harmonic oscillation
We have two possibilities.
- if we take a finite number and terms gives the same previous value
- If we take an infinite number of fears the series gives infinity and the average is also infinite
E_average= infinity
