What is a harmonic of oscillation (mode)? Give an explanation of different harmonics (modes).

(N/A) system of oscillations with a natural frequency is called a normal mode.
The possible minimum natural frequency is called the fundamental mode or first harmonic.
The frequency for a tensed string fixed at both ends forming a stationary wave is given by:
$v = \frac{n v}{2 L} \quad \dots (1)$
Substituting $v = \frac{v}{\lambda}$:
$L = \frac{n \lambda}{2} \quad \dots (2)$
And $\lambda = \frac{2 L}{n} \quad \dots (3)$ where $n = 1, 2, 3, \dots$
If $n = 1$,then:
$v_1 = \frac{v}{2 L}$,$L = \frac{\lambda_1}{2}$,and $\lambda_1 = 2 L$. Here,$v_1$ is called the fundamental frequency or first harmonic.
If $n = 2$,then:
$v_2 = \frac{v}{L} = 2 v_1$,$L = \lambda_2$,and $\lambda_2 = L$. Here,$v_2$ is called the second harmonic.
If $n = 3$,then:
$v_3 = \frac{3 v}{2 L} = 3 v_1$,$L = \frac{3 \lambda_3}{2}$,and $\lambda_3 = \frac{2}{3} L$. Here,$v_3$ is called the third harmonic.