The element values in the circuit are $R=2k,L=250mH,C=10nF.$ The initial current $I_0$ in the inductor is $-4$ A $,$ and the initial voltage on the capacitor is $0$ V $.$ The output signal is the voltage $v.$ Find

a$)i_R(0^{+})$;

b$)i_c(0^{+})$;

c$)dv\frac{0^{+}}{d}t$

d$)A_1$ :

e$)A_2$ :

f$)v(t)$ when $t0.$