EXAMPLE 12: Using Laplace transforms, find the solution of the initial value problem y" - 4y + 4y = 64 sin 2t y(0) = 0, y'(0) = 1 y" - 4y' + 4y = 64 sin 2t y(0) = 0, y'(0) = 1 Taking Laplace transform of both sides of (1), we have 64×2 5² +4 On putting the value of y(0) and y'(0) in (2), we get s²y-1-4s y+4y= 128 s² +4 Solution: [²y-sy(0)-y()]-4 y-y()]+ 4y = (²-45+4)y=1+ + 128 or (S-2) ÿ=1+ s +4 y=L* | -3 1 128 1 8 16 8s + (S-2) (s-2) (s²+4) (s-2) s-2 (S-2) s² +4 8.s 17 s-2 (S-2) s² +4 + y=-8e²¹ +17e²¹ +8 cos 2t 128 s² +4 Ans. (1) (2)

Find the frequency of a musical note which is 7 half-steps above a note with frequency 260 cps. Round to the nearest whole number. (Use the formula Q-Qo*1.05946" from your notes) The frequency of the note is cps.

What is x divided by 0?

A total of $6000 is invested for 5 yr with a total return of $1080. Part of the money is invested in a fund that returns the equivalent of 2% simple interest. The rest of the money is invested at 4% simple interest. Determine the amount invested in each account.