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.

2.which choice most accurately explains what happens to the bonds between atoms when water changes to steam, and what becomes of the energy added during this phase change? when water changes to steam bonds between molecules are created. after reaching the boiling point, energy is used to change bond strength and change the kinetic energy of the atoms. when water changes to steam bonds between molecules break apart. after reaching the boiling point, energy is used to break bonds, but does not affect the kinetic energy of the atoms. when water changes to steam bonds between molecules are created. after reaching the boiling point, energy is used to break bonds, but does not affect the kinetic energy of the atoms. when water changes to steam bonds between molecules break apart. after reaching the boiling point, energy is used to change bond strength and change the kinetic energy of the atoms.