1(a) Plot energy versus displacement for simple harmonic oscillator.

b) What is the condition of over-damping?

(c) Define impedance matching.

(c) Define impedance matching

**solution is provided at the bottom **

(d) A wave along a string is represented by y=0.02sin(30t-4-0x) meter where x is in meter and t is in second. What is the frequency of the wave?

(e) What are the conditions necessary for observing interference phenomenon?

Define stimulated emission of radiation.

(g) What do you mean by normalized wave function?

(h) Define principle. Heisenberg’s

uncertainty

(i) Two objects absolutely identical by their physical appearance, i.e., shape, size and colour. One of them is made up of metal and other one is of semi- conducting material. Suggest a suitable way to differentiate between them.

(J) what is Fermi energy?

Solve the equation of motion of a forced mechanical oscillator. How is velocity of forced oscillator related to the displacement? Plot velocity of a forced oscillator versus deriving frequency.

Q3. Write short notes on:

(a) Transverse wave on a string (b) Standing waves and their eigenvalues

Q4. Discuss reflection and transmission at boundary of two conducting media: Case of Oblique Incidence.

Q5. Write short notes on: (a) Newton’s ring

(b) Superposition of waves and interference of light by wavefront and amplitude

splitting

Q6. (a) Derive an expression for the intensity distribution due to Fraunhofer single- slit diffraction with its condition of principle maxima, secondary maxima and minima.

(b) What is Rayleigh criteria for the limit of resolution?

Q7. Write short notes on:

(a) Einstein’s coefficients and their relations (b) Ruby laser

Q8. Write short notes on:

(a) The Kronig-Penney model (b) Free-electron model of metals

Q9. Suppose a particle is trapped in the given potential ‘(x) =· 0; if 0≤x≤a ∞; if otherwise

Derive an expression for normalized wave function for this particle. What is the expectation value of the position of this particle?

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