Derive the expressions for the mean and variance of a geometric random variable with parameter p. (Formulas for infinite series are required.)

# Month: September 2021

## Derive The Expressions For The Energy And Energy Loss Curves Shown

Derive the expressions for the energy and energy-loss curves shown in Figure 3-8 for the damped oscillator. For a lightly damped oscillator, calculate the average rate at which the damped oscillator loses energy (i.e., compute a time average over one cycle).

## Derive The Expression For The Phase Paths Of The Plane Pendulum

Derive the expression for the phase paths of the plane pendulum if the total energy is E > 2mgl. Note that this is just the case of a particle moving in a periodic potential U (θ) = mgl (1 – cos θ).

## Derive The Expression For De Broglie Wavelength 955 Of

Derive the expression for a de Broglie wavelength λ of a relativistic particle moving with kinetic energy T. At what values of T does the error in determining λ using the non-relativistic formula not exceed 1 % for an electron and a proton?

## Derive The Disturbance Covariance Matrix For

Derive the disturbance covariance matrix for the model

What parameter is estimated by the regression of the OLS residuals on their lagged values?

## Derive Rate Expression For Each Of The Following

Derive a rate expression for each of the following single reactions taking place through a sequence of steps as indicated. Define your rate clearly. S represents an active site.

## Derive P3 X From The Rodrigues Formula And Check P3

Derive P3 (x) from the Rodrigues formula, and check that P3 (cos θ) satisfies the angular equation (3.60) for l = 3. Check that P3 and P1 are orthogonal by explicit integration.

## Derive In Cartesian Coordinates

Derive (in Cartesian coordinates) the quantum mechanical operators for the three components of angular momentum starting from the classical definition of angular momentum, l = r x p. Show that any two of the components do not mutually commute, and find their commutators.

## Derive Guideline 3 In Table 6

Derive Guideline 3 in Table 6.10 for a monatomic species of 30 amu:

a) Using collision theory and assuming a 2-dimensional gas.

b) Using absolute rate theory and assuming immobile adsorption.

c) Using absolute rate theory and assuming a 2-dimensional gas.

## Derive Expressions Shear Force V Bending Moment M And Sag

Derive expressions shear force V, bending moment M and sag w for a â€œweightlessâ€ beam with built-in ends of thickness h, breadth b and span L under a uniform load p. Plot the shear and moment diagrams. Use the sign convention that tension is positive, the x-axis is to the right, the z-axis down, the y-axis is out of the page, a ccw (counterclockwise) moment is positive and a downward shear force is positive as shown infigure.