Time : 3 Hours
Maximum Marks : 50
N.B. :— (1) All questions are compulsory and carry equal marks.
(2) Draw well labelled diagram wherever necessary.
1. (A) What is damped harmonic oscillator ? Derive the differential equation for it and obtain an
equation for its displacement. [5M]
(B) (i) Show that for damped harmonic oscillator total energy decreases exponentially with time. [3M]
(ii) A mass of 0.25 kg is suspended from the lower end of a vertical spring having force
constant 25N/m. The mechanical resistance of the system is 1.5N S/m. The mass is displaced
vertically and released. Find whether the motion is oscillatory. [2M]
(C) Obtain an expression for power dissipated in damped harmonic oscillators. [2½M]
(D) Define simple harmonic motion. Obtain general differential equation of simple harmonic motion. [2½M]
(E) Show that the resultant of two SHMs at right angles to each other having equal periods and
amplitudes but phase difference 90º is a circle. [2½M]
(F) A particle execute simple harmonic motion with time period of 5 sec. and amplitude 5 cm.
Calculate the maximum velocity of particle. [2½M]
2. (A) Derive the differential equation of forced harmonic oscillator. Solve the differential equation to
obtain steady state solution. [5M]
(B) (i) What is amplitude resonance ? Explain the effect of damping on it. [3M]
(ii) If the resonant frequencies of acoustic system is 280 Hz and half requencies are 200 Hz
and 360 Hz respectively, calculate quality factor. [2M]
(C) What is quality factor ? Give the physical significance of quality factor of forced oscillator. [2½M]
(D) Show that Resonance absorption bandwidth $Latex \left(P_2-P_1\right)=\frac Rm$ [2½M]
(E) What is piezoelectric effect ? Discuss one of its application. [2½M]
(F) A damped oscillator of mass 2 × 10–3 kg and force constant 500N/m is subjected to a periodic
force of variable frequency. Find the frequency of force for the velocity resonance. If the mechanical
resistance 2 × 10–3 Ns/m, calculate quality factor for the oscillator. [2½M]
3. (A) What are the transport phenomena in gases ? Derive an expression for coefficient of diffusion of
a gas. [5M]
(B) (i) State and prove law of equipartition of energy. [3M]
(ii) Calculate the diameter of a molecule, if n = 2.79 × 1019 molecule per c.c. and mean free
path l = 2.2 × 10–6cm. [2M]
(C) Define mean free path. Discuss the effect of temperature and pressure on mean free path. [2½M]
(D) Derive the expression for coefficient of viscosity of gas on the basis of transport phenomenon of gas. [2½M]
(E) Derive the equation for van der Waal’s constant a and b. [2½M]
(F) Calculate critical pressure of gas having van der Waal’s constant a = 0.58 Nm4/kg mole2 and
b = 0.0316 m3/mole. [2½M]
4. (A) What is Joule-Thomson effect ? Derive the expression for Joule-Thomson co-efficient. [5M]
(B) (i) Define entropy. Show that change in entrophy in reversible cycle is zero. [3M]
(ii) Calculate the change in entropy when 1kg of water is raised from 0ºC to 100ºC, Sp. heat
capacity of water is 1 kcal/kg k. (1 kcal = 4184 J). [2M]
(C) Write down the difference between reversible process and irreversible process. [2½M]
(D) State first law of thermodynamics. Give the importance and limitations of it. [2½M]
(E) Show that in irreversible process, entropy always increases. [2½M]
(F) A Carnot engine working in a cycle absorb 100 kcal. If the temperature of source and sink are
327ºC and 27ºC, calculate the heat rejected to the sink. [2½M]
5. Attempt any TEN questions : 1×10M
(i) What is Liassajous Figure ?
(ii) Define free oscillation.
(iii) A mass of 1kg is attached to a spring of force constant 16N/m. Find its natural frequency.
(iv) What is velocity resonance ?
(v) Define mechanical impedance.
(vi) Show that the unit of damping coefficient ‘b’ is sec–1.
(vii) State Boyle’s law.
(viii) Define self diffusion.
(ix) Define critical temperature and critical pressure.
(x) Write down the expression for Clausius-Claperon equation.
(xi) What is cyclic process ?
(xii) State third law of thermodynamics.