energy U 8.10 Show that in LC corent, the total can be written as [ 0...
2. Show that W can be written as where U is the number of pairs (Xi, Yj) with X, < Y,. In other words n m U=ΣΣ1," where ,j -(0 otherwise. i=1 j=1 Hint: Let Yi),Ya),... , Ym) be the order statistics for the y-sample. Then U is the number of pairs (Xi,Yu)) with Xi 〈 YG). For fixed j , the number of Xi with Xi 〈 Yu) is just the rank of Y (j) minus the number of...
Can you answer parts a-c In a certain oscillating LC circuit, the total energy is converted from electrical energy in the capacitor to magnetic energy in the inductor in 2.22 mu s. What are (a) the period of oscillation in microseconds and (b) the frequency of oscillation? (c) How long after the magnetic energy (in microseconds) is a maximum will it be a maximum again? (a) Number Units (b) Number Units (c) Number Units
please solve B? and C) The total energy for the vibrating string problem can be written as E = Kinetic Energy + Potential Energy = dx. Consider the case where u(r, t) satisfies the wave equation with the boundary con ditions ux(0,t) 4(L, t)-0. (a) Show that E is constant in time (b) Calculate the energy in 1 mode. (c) Show that the total energy is the sum of the energies contained in each mode
-14 Points WE ALS KAIZESEI 35.F.US. In the LC circuit in the figure below, the inductance is L-21.4 mH and the capacitance is C - 20.0 ml. At some moment, Ug UE-45.0 m). Capacitor initially fully charged; switch open S I=0 le с L& (a) What is the maximum charge stored by the capacitor? с (b) What is the maximum current in the circuit? A (c) Att - 0, the capacitor is fully charged. Write an expression for the charge...
3) An ideal LC circuit comprises an ideal inductor having inductance L, a capacitor having capacitance C, and a switch. The circuit does not include a battery nor does it include any resistance. The switch is initially open and the initial charge on the capacitor is Qo. The switch is closed at time 1-0. Show that the charge, 4, on the capacitor is given by the time dependent function 9(t) = Qocos(at) where o is given by W= Hint: Apply...
Use strong induction to show that every positive integer can be written as a sum of distinct powers of two (i.e., 20 = 1; 21 = 2; 22 =4; 23 = 8; 24 = 16; :). For example: 19 = 16 + 2 + 1 = 2^4 + 2^1 + 2^0 Hint: For the inductive step, separately consider the case where k +1 is even and where it is odd. When it is even, note that (k + 1)=2 is...
The internal energy, U, is the total energy of a system. For any isolated system, the internal energy is constant. U is a state function, meaning that any path used in calculating AU ill result in the same answer. For any pure substance or fixed mixture of substances, the internal energy, U, can be determined from any two of the variablesP, V, and T. It is often most convenient to choose V and T as the variables. It is helpful,...
Prove that the total gravitational potential energy can be written as ρ(z)φ(z)dr, where ρ(z) and φ(z) are the density and gravitational poi.(.mi.ial ai. locai;ion x in space, Π iptXtively Use the above formula for W to obtain the total gravitational energy of the Plummer sphere with the graviational potential: φ(r) = (r2+p)
1. (30pt) LC Circuit and Simple Harmonic Oscillator (From $23.12 RLC Series AC Circuits) Let us first consider a point mass m > 0 with a spring k> 0 (see Figure 23.52). This system is sometimes called a simple harmonic oscillator. The equation of motion (EMI) is given by ma= -kr (1) where the acceleration a is given by the second derivative of the coordinate r with respect to time t, namely dr(t) (2) dt de(t) (6) at) (3) dt...
Consider the circuit below, we can show: 522 10u(-1) V 2012 05H3, i(t)= 2e-8t u(t) A The steadystate inductor energy for t> 0 is 1 The initial inductor power p(0) = 16 W The steady-state inductor energy fort > O is OJ