Four masses connected by Euler-Bernoulli bearns and resting on springs form a tirnpilied madel of a bridge. The masses a

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Four masses connected by Euler-Bernoulli bearns and resting on springs form a tirnpilied madel of a bridge. The masses a

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Four Masses Connected By Euler Bernoulli Bearns And Resting On Springs Form A Tirnpilied Madel Of A Bridge The Masses A 1
Four Masses Connected By Euler Bernoulli Bearns And Resting On Springs Form A Tirnpilied Madel Of A Bridge The Masses A 1 (34.44 KiB) Viewed 41 times
Four Masses Connected By Euler Bernoulli Bearns And Resting On Springs Form A Tirnpilied Madel Of A Bridge The Masses A 2
Four Masses Connected By Euler Bernoulli Bearns And Resting On Springs Form A Tirnpilied Madel Of A Bridge The Masses A 2 (43.47 KiB) Viewed 41 times
Four masses connected by Euler-Bernoulli bearns and resting on springs form a tirnpilied madel 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 satisly a pair of socond order simultaneous differential equations: dt2d2w1​​=aw1​+bw2​dt2d2w2​​=cw1​+du2​​ Where a=−151,b=15,c=−1,350,d=134 (a) What is the smaller of the fwo normal mode angular frequencies? If your answor is not an integer (whole namber), glve it to AT LEAST THREE PLACES OF DECIMALS. Put in this value only ie. Leave out any letters (2 marks) This question accepts numbers of formulas: Piot 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. Loave out any letiers (2) marks) This question accepts numbors 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 ditterential equations which satisfy the initial displacements w 1 = 13 and wh =−9 at t = B. For this part of the question give w1​ as a function of t. Leave out the "w w1​= " (5 marks)
(d) What is w2​ as a function of t ? Leave out the "w 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 (7) 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 " th 2= " (1 mark) This question accepts numbers or formulas. Piot I Help I Switch to Equation Editor I Preview (a) 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 le. Leave out any letters (2 marks) This question accepts numbers or formulas. Piot 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 trequency? Give your answer to AT LEAST FOUP PLACES OF DECIMALS. Put in this value only le. Leave out any letters (2 marks)
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