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Normal Modes : Second Order Simultaneous Equations

This question is concerned with finding the solutions of the second order simultaneous equations

where a = 38, b = -9, c = 378, d = -79

(i) Find the particular solutions to the differential equations which satisfy the initial conditions x = -10 and y = 7 at t = 0
together with the condition at t = 0..
For this part of the question give x as a function of t.
Omit the "x = " (8 marks)

Your Answer: -77(cos(4t))+ 67(cos(5t))
Comment: The particular solution required in this part is x = ""

(ii) What is y as a function of t.
Omit the "y = "
(8 marks)

Your Answer: -462(cos(4t))+ 469(cos(5t))
Comment: The particular solution required in this part is y = ""

(iii) What is the value of x at t = 0.56?
Give your answer to AT LEAST TWO PLACES OF DECIMALS. Put in this value only ie. Omit the "x = " (2 marks)
Your Answer: -15.36105271
Comment: x = -15.36105271

(iv) What is the value of y at t = 0.56?
Give your answer to AT LEAST TWO PLACES OF DECIMALS. Put in this value only ie. Omit the "y = " (2 marks)
Your Answer: -155.2952131
Comment: y = -155.2952131

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Second Order Simultaneous Equations are investigated. The solution is detailed and well presented. The response received a rating of "5" from the student who posted the question.

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