USN t0nllB72 Seventh Semester B.E. Degree Examination, Dec. 20l3lJan.2Ol4 Mechanical Vibrations Time: 3 hrs. Max. Marks:100 N ote : a y w y-!!,(r fu il, 1 u estj on s, s e I yct i n g. otleast TWO questions from each part. PART _ A PART _ A I a. With a sketch, explain the beats phenomenon and obtain its resultant motion. (10 Marks) b. If x(t): uo + Lancosnwt*IU"cosnwt, where x(t) us apefiodic, nonharmonic, obtain n=l n=l expressions for a6, all and bp. (10 Marks) (10 Marks) (10 Marks) o o o L C) (! (.) Eq z Jh - bol i00 .= c{ 9d otr aO o2 ;:: oO a0< a6 'l,6 4o 'Ca oj5 o-E oj 9E to 6LE LO JE >, li b0- c olJ a= Xo VL o_ U< ,r.' C.i () o 2 a. What is the effect of mass of a spring on its natural frequency? Derive. b. Find the natural frequencies of Fig. Q2(b). , Fig. Q2(b) For an under dar'nped system, derive an expression of A vibratingrsystem having a mass 3 kg, spring stiffness of 100 N/m and damping coefficient of 3 N - sec/m. Determine damping ratio, damped natural frequency, logarithmic decrement, ratio of two consecutive amplitudei and number of cycles after which the original amplitude (10 Marks) (08 Marks) Discuss the (10 Marks) (10 Marks) 4a. b. is reduced to 20Yo. (10 Marks) Analyse the undertamped system subjected to constant harmonic excitation and show the complete solution. (12 Marks) A vibrating system having mass 100 kg is suspended by a spring of stiffness 19600 N/m and is acted upon by a harmonic force of 39.2 N at the undamped natural frequency. Assuming visious damping with a coefficient of 98 N - sec/m. Determine resonant frequency, phase angle at resonance, amplitude at resonance, the frequency corresponding to the peak amplitude and damped frequency PART _ B 5 a. Mention the instruments used to measure displacement and acceleration. relevant frequency response curves. b. Derive an expression for amplitude of a whirling shafts with air damping. 1 r'rf') For More Question Papers Visit - www.pediawikiblog.com For More Question Papers Visit - www.pediawikiblog.com www.pediawikiblog.com