Answer
a) ${\bf50}\;\rm Hz$
b) ${\bf 1.59}\;\rm mH$
Work Step by Step
$$\color{blue}{\bf [a]}$$
We know that the frequency is given by
$$f=\dfrac{1}{T}$$
where, from the given graphs, the period is 0.02 s.
$$f=\dfrac{1}{0.02}=\color{red}{\bf50}\;\rm Hz$$
$$\color{blue}{\bf [b]}$$
Recalling that the inductor voltage is given by
$$V_L=I_LX_L$$
where $X_L= \omega L$, so
$$V_L=I_L\omega L =2\pi f I_LL$$
Hence the inductance is given by
$$L=\dfrac{V_L}{ 2\pi f I_L} $$
We can see, from the given graph, $I_L=2.0$ A, and $V_L=1.0$ V.
Plug the known;
$$L=\dfrac{1.0}{ 2\pi (50)(2)} $$
$$L=\color{red}{\bf 1.59}\;\rm mH$$
