Question 1 In a two mass, two spring system, the displacements of the two masses are represented by z(t) and y(t) at time t. The motion is governed by the following pair of second order simultaneous differential equations: 24 points d²r = ax + by dt2 d²y =cx+dy dt2 where a=-7, b = -3,c=6,d=2 (a) The system is initially released from rest. Find the particular solutions to the differential equations which satisfy the initial displacements x=11 and y=-20 at t=0. For this part of the question give x as a function of t Omit the "x="(8 marks) This question accepts numbers or formulas. Plot | Help | Switch to Equation Editor | Preview (b) What is y as a function of t. Omit the "y=" (8 marks) This question accepts numbers or formulas. Plot | Help | Switch to Equation Editor | Preview (c) What is the value of x at t=0.38? Give your answer to AT LEAST THREE PLACES OF DECIMALS. Put in this value only ie. Omit the "x = " (2 marks) This question accepts numbers or formulas. Plot | Help | Switch to Equation Editor | Preview (d) What is the value of y at t=0.38? Give your answer to AT LEAST THREE PLACES OF DECIMALS. Put in this value only ie. Omit the 'y =" (2 marks) This question accepts numbers or formulas. Plot | Help | Switch to Equation Editor | Preview (e) What is the period of oscillation in the normal mode corresponding to the larger angular frequency? Give your answer to AT LEAST THREE PLACES OF DECIMALS. Put in this value only ie. Omit any letters (2 marks) This question accepts numbers or formulas. Plot | Help | Switch to Equation Editor | Preview (f) What is the period of oscillation in the normal mode corresponding to the smaller angular frequency? Give your answer to AT LEAST THREE PLACES OF DECIMALS. Put in this value only ie. Omit any letters (2 marks) This question accepts numbers or formulas. Plot | Help | Switch to Equation Editor | Preview