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Thursday, March 4, 2021

B.A./B.Sc. (General) 1st Semester
Paper-B: Vibrations, Waves & E.M. Theory-I 

Time Allowed: Three Hours) (Maximum Marks: 22 


(1) Attempt five questions in all, selecting two  questions each from Section-A and B. Section-Cis compulsory 

(2) Use of a non-programmable calculator is allowed.


1. (a) Discuss composition of two SHM perpendicular to each other and periods are in the ratio 1:2. 

(b) A body stands on a platform which vibrates simple harmonically in a vertical direction at a frequency of 5 Hz. Show that the body loses contact with the platform when displacement exceeds 10-2 meters. 3, 1.5 

II. (a) Write and solve the differential equation for a damped LCR circuit and discuss the oscillatory discharge of the capacitor. 

(b) Find the frequency and quality factor of a circuit having

L = 2 mH, C = 5 uF and R = 0.2 ohm. 3, 1.5

III. What is a compound pendulum? Derive an expression for its time period. What is the condition for time period to be a minimum? 4.5 


IV. (a) Find expression for the quality factor of a forced oscillator in terms of resonance absorption band width. 

(b) What is mechanical impedance of a forced oscillator? Write expression for it, explaining the meaning of each term. 3.5.1 

V. (a) Discuss the oscillations of two pendulums coupled through a spring of stiffness S and write the equations of motion of the system in different cases. 

(b) Show that in a resonant LCR circuit, the maximum potential drop occurs across the capacitor at a frequency:   

VI. Write down the equation of motion of a forced oscillator being driven by an alternating force F cos wt. Explain its steady state behaviour and hence describe the behaviour of displacement versus driving force frequency. 4.5


VII. Attempt any eight parts :

(a) Explain the role of restoring force and inertia in SHM. 

(b) A mass of 1 kg is attached to a spring of stiffness constant 25 Nm-1 Find the natural frequency. 

(c) How the logarithmic decrement is related to quality factor? 

(d) Is energy stored in a forced oscillator? Explain 

(e) What is meant by transient state of a forced harmonic oscillator? 

(f) What is the effect of damping on the natural frequency of an oscillator? 

(g) Why does an LC circuit usually produce damped oscillations? 

(h) Why the glass windows may be broken by the far away explosion? 

(i) Is the transformer loose or tight coupled, whose mutual inductance is 0.3 H and self-inductance of primary and secondary are 0.25 H and 4.0 H respectively? 

(j) What is importance of normal modes of vibration? 1/2x8=4




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