Question

Derive the governing equation of motion for the angular motion of a bar suspended using bifilar suspension, and hence, derive the expression for the angular frequency.

Answer 1

STRING l ILTI Tai -2.22 CG7 B' 00 01 = l, o T202 TOI In a 61 Filar suspension, a body of weight is suspended l, o=e0, by two strings. This method is used in laboratooy to experimentally determine the e moment of inertia of and l20= 102 loregularly shaped bodies or 02=l20 l The body orginally occupying Position AB, when given an Tension Ti and Tz in the angular twist o and released two string cocecute torsional viooation: Ti [li+l2] = wlz Will T= Wlz litla Let G be the CG of the body li, lz are the distances of two ends of the string from CG respectively and Ai, Oz be the angular displacement of the string from vertical and Tz [l,+ lz]= wei T2= Wli litle foom geometoy of the figure For small angles CS5canned with CamScanner

for small angles Di, 02 Toi I denotes moment of inertia and Tzd2 are the components of the body about CG and of tension in the horizontal Iö is inertia tooque direction which act Ly Iö + While o=0 to A'B'. e (Ans) The resisting torque To For since I=mk² miköt Welzo=0 the system (Ans) e To = (1, 0)2, + (12 Oz) lz Natural Frequency Wn Weilz substituting the values of (Ans) e Ti & T2 in the above Equation & also suosti- K= Wlilz gl, lz tuting 0,8 02 mewn en? ve (mk?) To= Wlz + 0:+82)64 glas, Wei (lzo +2) l = W8, 220 (21+22) e (li+12) ܘܬܨ?To : W To = Wl, le l The Equation of toosional vibration of the body IÖ + To 20 CS Scanned with CamScanner