Please help me solve these physics questions Please show you

Please help me solve these physics questions. Please show your work and explain your answer.

Thank you! I have included the questions, as well as the material for them.

Solution

A)

Inductive reactance, Xl = 2*pi*fL

= 2*pi*80*0.025

= 12.6 ohm

Capacitive reactance:

Xc = 1/(2*pi*f*C) = 1/(2*pi*80*100*10^-12)

= 1.99*10^7 ohm

So, impedance, Z = sqrt(R^2 +(Xl - Xc)^2)

= sqrt(5000^2 + (1.99*10^7 - 12.6)^2)

= 1.99*10^7 ohm

Natural mode angular frequency :

W = (1/sqrt(LC))*sqrt(1-(R^2/4)*C/L)

= (1/sqrt(0.025*100*10^-12))*sqrt(1-(5000^2/4)*100*10^-12/0.025)

= 6.245*10^5 rad/s

So, natural mode frequency = W/(2*pi) = 6.245*10^5/(2*pi)

= 9.939*10^4 Hz

Oscillation angular frequency, Wo =  (1/sqrt(0.025*100*10^-12))

= 6.32456*10^5 rad/s

So,

oscillation frequency = 6.32456*10^5/(2*pi) = 1.00659*10^5 Hz

B)

5 major divisions cover 10*5 = 50 us

So, time period for 1 oscillation = 50/5 = 10 us

So, frequency , f = 1/T = 1/(10*10^-6)

So, f = 1*10^5 Hz <-----answer

As the small division is 0.2 times the major division. So, the oscillation frequency obtained in part 1 is less than 0.2 times the value obtained in this section.

So, it is indistinguishable..