To understand how the two standard ways to write the general solution to a harmonic oscillator are related. There are two common forms for the general solution for the position of a harmonic oscillator as a function of time t:

x(t)=Acos(ωt+ϕ) and
x(t)=Ccos(ωt)+Ssin(ωt).

Either of these equations is a general solution of a second-order differential equation (F⃗ =ma⃗ ); hence both must have at least two--arbitrary constants--parameters that can be adjusted to fit the solution to the particular motion at hand. (Some texts refer to these arbitrary constants as boundary values.)

Required:
a. Find analytic expressions for the arbitrary constants C.
b. Find analytic expressions for the arbitrary constants A and ϕ.

Which type of circuit is becoming more common in residential electrical design and construction? a. hazardous-area circuit b. three-phase circuit c. 480-volt circuit d. communication circuit

Suppose that an electromagnetic wave which is linearly polarized along the x−axis is propagating in vacuum along the z−axis. the wave is incident on a conductor which is placed at z > 0 region of the space. the conductor has conductivity σ, magnetic permeability µ and electric permittivity ε. (a) find the characteristic time for the free charge density which dissipates at the conductor. (b) write the maxwell equations and derive the wave equation for a plane wave propagating in a conductor. (c) find the attenuation distance at which the incident amplitude reduces to e ^−1 of its initial value. (d) find the electric and magnetic fields inside the conductor. 8 (e) find the power loss per area of the incident electromagnetic wave at the surface of conductor.

What is the momentum of a 2 kg object moving at 15 meters per second