Four masses connected by Euler-Bernoulli beams and resting on springs form a simplitied model of a bridge. The masses at

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Four Masses Connected By Euler Bernoulli Beams And Resting On Springs Form A Simplitied Model Of A Bridge The Masses At 1 (41.1 KiB) Viewed 47 times

Four masses connected by Euler-Bernoulli beams and resting on springs form a simplitied model of a bridge. The masses at ends of this structure are clamped and the middie two masses vibrate having displacements v1​(t) and w(t) at time t. These functions satisty a pair of second order simultaneous differential equations: dt2d2w1​​=aw1​+bw2​dt2d2w2​​=cw1​+dw2​​ where a=−151,b=15,c=−1,350,d=134 (a) What is the smaller of the two normal mode angular frequencies? If your answer is not an integer (whole number), give is to AT LEAST THREE PLACES OF DECIMALS, Put in this value only ie. Leave out any letters (2. marks) This question accepts numbers or formulas. Plot I Help I Switch to Equation Editor I Preview (b) What is the larger of the two normal mode angular trequencies? If your answer is not an integer (whole number), give it to AT LEAST THREE PLACES OF DECIMALS. Put in this value only le. Leave out any lotters (2. marks) This question accepts numbers or formulas. Plot I Heip I Switch to Equation Editor I Previow (c) The system is initialily at rest. Find the particular solutions to the differential equations which satisfy the initial displacements w1=13 and w2=⋅9 at t= 0 . For this part of the question give w1​ as a function of t. Leave out the "w w1​= " (5 marks ).