This sequel of the previous problem will remind you of how you find small oscillations of a classical system near its equilibrium point (they are will teach you how to treat them quantum mechanically to estimate the first few energy eigenvalues of the system, and will train you in making order of magnitude estimates a) assume that the pendulum of the previous problem performs small oscillations around its stable equilibrium point θ-0. approximate the potential energy around this point with a harmonic oscillator potential and find the classical frequency of such small oscillations. b) write the quantum hamiltonian of the pendulum for such small oscillations and find the energy spectrum of these small oscillations. (the energy levels must be expressed in terms of the constants 1, u and ћ.) c) the oscillating molecule is in its first excited state and decays into its ground state by emitting one photon. using the approximation of the previous part, determine the wave- length of the photon.

we have been given a quadratic function and we need to restrict the domain such that it becomes a one to one function.

we know that vertex of this quadratic function occurs at (5,2).

further, we know that range of this function is .

if we restrict the domain of this function to either or , it will become one to one function.

let us know find its inverse.

upon interchanging x and y, we get:

let us now solve this function for y.

hence, the inverse function would be if we restrict the domain of original function to and the inverse function would be if we restrict the domain to .

there are no components of a physical goal mentioned on the list of choices that you've provided.

the answer is the first electromagnet (a). this is because it has more coils around the ferromagnetic material. increasing the number of coils increases the surface area in which the metal interacts with the current in the coil. this enables more atoms in the metal to become aligned hence becoming more magnetized.

you'd use the equation that establishes a relationship between  energy  and  wavelength, which looks like this

e=h⋅cλ, where

λ  - the wavelength of the photon; c  - the speed of light, usually given as  3⋅108m/s; h  -  planck's constant, equal to  6.626⋅10−34j s

plug the value you were given for the energy of the photon in the above equation to get the wavelength

e=h⋅cλ⇒λ=h⋅ce

λ=6.626⋅10−34js⋅3⋅108ms−1.257⋅10−24j=1.581⋅10−1m