TRUING DAI HQC SU' PHAM KY THU AT
t h An h PHO HO CHI MINH
KHOA CO KHI CHE TAO MAY
BO MON CO DIEN TU'
DE THI CUOI KY HQC KY I (2023 - 2024)
Mon: TOAN iTNG DQNG CO KHI (Dai Tra)
Ma mon hgc: AMME131529
B6 so/Ma de: 01 Be thi co 02 trang
Thai gian: 90 phut Ngay thi 18/12/2023
SV chi dugc phep sir dung mot to A4 chep tay.
Cau 1: (3,0 diem)
Mo hinh toan hoc cua mot he thong co khi dugc mo ta bdi phuong trinh vi phan nhu sau:
mx"(t) + bx'(t) + kx(t) = r(t)
Bietkhoi lugng m = 1/9 (k g ), he s6 giam chan b = 4^9 ^N s/rnj, do cirng 16 xo k = 5^9 (N/rnj
Voi vi tri va van toe ban dau la x(0) = 0, x(Q) = 0, va tin hieu dau vao r(t) = t, 0 < t < 3
t + 2, t,> 3
a. Tim bien doi Laplace R(s)
b. Tim bien doi Laplace X(s)
c. Tim tin hieu dao dong x(t)
Cau 2: (2,0 diem) Cho phuong trinh vi phan va dieu kien ban dau nhu sau:
^ = ~ M + y \ te [l,2 ],y ( l) = - 2
at t v '
Hay tim gia tri y(t) bdng phuong phap Runge-Kutta bac 3 voi buoc tinh la h = 0.2 (tinh chinh xac
den 4 chu so thap phan).
Cau 3: (2,0 diim) Gia trj dien ap V{volt) do dugc cua mot cam bien do khoang each dugc cho nhu
bang ben duoi:
D(cm) 20 40 50 60 70 90
V (volt) 2.55 1.55 1.25 1.05 0.88 0.7
Hay uoc lugng gia trj dien ap F(volt) cua cam bien 6 khoang each 42 cm theo phuong phap noi suy
Newton cho da thirc bac 3 (tinh chinh xac den 4 chu so tftap phan).
Cau 4: (3,0 diem) Cho h? phuong trinh dai so tuyen tinh sau:
- x x + 2x2 + 2x3 = 0
2xx + 2x2 + j3x3 — 1 (1)
2xx + ax2 + 2x3 = -1
a. Viet lai he phuong trinh (1) duoi dang Ax — B, voi x = [xx x2 x:i]T, B — [0 l ~ l]r . Tim
dieu kien cua a,/3 de ton tai ma tran A~l
b. Tinh ma tran A~l tu do suy ra gia tri x = \xx x2 x f , biet A la ma tran doi xung va (3 — — 1
c. Tim trj rieng va vec to rieng cua m& tran A a cau b.
HET.
Ghi chu: Can bo coi thi khong duac giai thich de thi.
So hieu: BM1/QT-PBT-RDTV/02 Lan soat xet: 02 Ngay hieu luc: 15/5/2020 Trang: 1/2
O m an dau ra cua hpc phan (ve kien thu c) N§i dung kiem tra
[CLOl]: Co kha nang ap dung cac phuong phap bien doi Laplace va cac
phuang phap so gan dung (Euler, Euler cai tien, Runge-Kutta) de giai cac
bai toan phuffng trinh vi p han dupe mo hinh hoa tu cac he thong co khl,
ca dien tu.
Cau 1
Cau 2
[CL03]: Co kha nang ap dung cac phuang phap noi suy da thuc
(Lagrange, Newton, Spline) de ude luo ng gia trj dap ung cua he thong
ky thuat.
Cau 3
[CL04]: Co kha nang ap dung cac kien thuc ve ma tran nhu djnh thuc
cua ma tran, ma tran nghich dao, trj rieng, vec ta rieng,..., de giai duo'c
cac bai toan ky thuat lien quan den djnh thurc ma tran.
Cau 4
Ngayl4 thang 12 nam 2023
Trirdng bo moil
S6 hi?u: BM1/QT-PBT-RDTV/02 Lan soat xet: 02 Ngay hieu luc: 15/5/2020 Trang: 2/2