The Langevin equation for a particle in 1 dimension in an external potential V (x) is: mx'' =-(dV(x)/dx)-ξx'+F(t), where ξ is the friction constant, and F(t) is the random force.Take V (x) to be harmonic: V (x) = (m/2)ω^2x^2 .Find the general solution x(t) for arbitrary initial conditions and calculate the equilibrium time correlation function C(t) = <x(t)x(0)>.

Consider the following half reactions at 298 K

Fe²⁺ + 2 e^- → Fe    E^o = -0.441 V
Cd²⁺ + 2 e^- → Cd    E^o = -0.403 V

A galvanice cell based on these half reactions is set up under standard conditions where each solution is 1.00 L and each electrode weighs exactly 100.0 g. How much will the Cd electrode weigh when the nonstandard potential of the cell is 0.02804 V?

Part A:

Rank these transition metal ions in order of decreasing number of unpaired electrons. If two ions have the same number of unpaired electrons, overlap them such that the two appear in a single column:

Consider the following vanadium species. Arrange them in order of strongest to weakest oxidizing agent:

1.      Which of the following must be satisfied by the flow of any fluid, real or ideal?

I. Newton's second law of motion

II. the continuity equation

III. the requirement of a uniform velocity distribution

IV. Newton's law of viscosity

V. the principle of conservation of energy

a)      I, II, and III

b)      I, II, and IV

c)      I, II, III, and N

d)      I, II, and V

e)      I, II, N, and V

a. Find the average and rms values of the current i(t) = 6 + 10 sin ωt A.
Vb in the voltage-regulator circuit below varies by ± 10 % from its nominal value of 12 V. If the circuit has a constant reverse breakdown voltage
VZ = 8.2 V for 75 mA ≤ iZ ≤ 1 A.
b. Obtain RS that will maintain vL = VZ = 8.2 V
c. Determine iZ ≥ 75 mA at the lowest value of Vb

Which of the following will increase renal filtration i.) decreasing the radius of the afferent arteriole ii.) increasing the radius of the afferent arteriole iii.) decreasing the radius of the efferent arteriole iv.) increasing the radius of the efferent arteriole v.) increasing the blood pressure vi.) decreasing the blood pressure. A.) i, iv and v B.) ii, iii and v C.) ii, iv and vi D.) i, iii and vi E.) ii, iii and vi

Identify the define node, usage node, du-paths and dc-paths for all the variables.

int binsearch(int x,int v[],int n)
{
    int low,high,mid;

    low=0;
    high=n-1;

    while(low<high)
    {
        mid = ( low + high ) / 2;

        if( x < v[mid])
            high  = mid - 1;
        else if ( x > v[mid])
            low = mid + 1;
        else
            return mid;
    }
    return -1;
}

W represent the wingspan of an airplane and V represents the velocity which are 2 random variables.
W has a normal distribution with mean 10 and standard deviation 4.
Also V = 0.5.W + U, where U is a random variable (we might call error). Assume that U has a standard normal distribution and is independent of W. Derive each element of the variance-covariance matrix for W and V using properties of Variance and Covariance.

A series RLC circuit connected to a 24-V AC source has a current of 150 mA when the AC source is set to 85 Hz. The voltage on the capacitor is measured to be 36 V. When the frequency of the source is adjusted in any way the current decreases. Calculate the values of R L, and C.

In P4, the frequency of the AC source is increased until the voltage on the capacitor has dropped to 12 V. Calculate the voltage on the inductor at this frequency

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You wire a real battery to a R1 = 42 Ω resistor and find that the output voltage between its terminals is V1 = 8.6 V. You disconnect it from the first resistor, wire it to a R2 = 720 Ω resistor, and find that its output voltage is V2 = 9.7 V. (a) Determine the current through each resistor. I1 = I2= (b) Find the internal resistance and emf of the battery. r = Ω e m f = V