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

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

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Four Masses Connected By Euler Bernouli Beams And Resting On Springs Form A Simplified Model Of A Bridge The Masses At 1
Four Masses Connected By Euler Bernouli Beams And Resting On Springs Form A Simplified Model Of A Bridge The Masses At 1 (45.55 KiB) Viewed 40 times
Four Masses Connected By Euler Bernouli Beams And Resting On Springs Form A Simplified Model Of A Bridge The Masses At 2
Four Masses Connected By Euler Bernouli Beams And Resting On Springs Form A Simplified Model Of A Bridge The Masses At 2 (58.6 KiB) Viewed 40 times
Four masses connected by Euler-Bernouli beams and resting on springs form a simplified model of a bridge. The masses at ends of this structure are clamped and the middle two masses vibrate having displacements w1​(t) and w2​(t) at time t. These functions satisfy 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 it to AT LEAST THREE PLACES OF DECIMALS. Put in this value only ie. Leave out any letters (2 markș) 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 frequencies? If your answer is not an integer (whole number). give it to AT LEAST THAEE 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 (c) The system is initially at rest. Find the particular solutions to the differential equations which satisfy the initial displacements w1​ = 13 and wh=−9 at t =0. For this part of the question give w1​ as a function of t. Leave out the " w1​= " (5 marks)
(d) What is w2​ as a function of t ? Leave out the " w2​= " (5 marks) This question accepts numbers or formulas. Plot I Help I Switch to Equation Editor I Preview (e) What is the value of w1​ at t=0.26 ? Give your answer to AT LEAST FOUR PLACES OF DECIMALS. Put in this value only ie. Leave out the " w1​="(1 mark) This question accepts numbers or formulas: Plot I Help I Switch to Equation Editor I Preview (f) What is the value of w2​ at t=0.26 ? Give your answer to AT LEAST FOUR PLACES OF DECIMALS. Put in this value only ie. Leave out the " w2​=∗(1 mark) This question accepts numbers or formulas. Plot I Help I Switch to Equation Editor I Proview (g) What is the period of oscillation in the normal mode corresponding to the larger angular frequency? Give your answer to AT LEAST FOUR PLACES OF DECIMALS. Put in this value only ie. Leave out any lotters (2 marks) This question accepts numbers or formulas. Plot I Help I Switch to Equation Editor I Preview (h) What is the period of oscillation in the normal mode corresponding to the smaller angular frequency? Give your answer to AT LEAST FOUR PLACES OF DECIMALS. Put in this value only ie. Leave out any letters (2 marks)
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