MTH401 Quiz 1

Mth401 Midterm quiz · Lecture 11 to 20 Quiz 2 · ORANGE MONKEY TEAM

1. If we want to solve an initial value problem then we need to apply the initial conditions to the ___ solution and not to the complementary function alone

General….confirm

2. The input function g(x) can have one of the forms A constant function k A polynomial function

All options are correct…confirm

Q3. How are frequency and period related in simple harmonic motion?

They are inversely related…..confirm

4. The displacement measured below the equilibrium position are _____.

Positive….confirm

5. If the auxiliary equation am2 + bm + c = 0 has two unequal real roots m1 and m2 then the solutions of the differential equation ay + by + cy = 0 could be __________.

…..confirm

6. If the auxiliary equation m3 + m = 0 has roots m = 0, m = +I then the complementary function is

yc = c1cosx + c2sinx…..confirm · 7. What is annihilator operator of the function g(x) = 8e3x · D- 3

Q8. If y = 2 + x then which of the following is true for it?

Its annihilator operator is D2

9. The auxiliary equation of the differential equation y’’’ + 2y’’ – 3y = 0 is

m3+2m2-3=0…..confirm

10. The hook’s law states that the force F is proportional to the

Elongation…..confirm

11. The solution of the auxiliary equation determines the ______ of the differential equation

Solutions….confirm

12. The gravitational force exerted by the earth on a body of mass m is called ______of the body

Weight….confirm

13. An annihilator operator L for the function f(x) = e3x is L = _______.

D-3….confirm

14. If y=e(1/2)x(c1cos (root(3)/2)x + c2sin (root(3)/2)x) is the complementary solution of y’’ – y’ + y = 2 sin 3x then the general form of its particular solution is yp _________.

A cos3x + B sin3x

15. The roots of the auxiliary equation , m2 – 10m + 25 = (m – 5)2 = 0 for a differential equation is __________.

M1 = m2 = 5

16. The roots of the auxiliary equation , 2m2 – 5m - 3 = (2m +1) (m – 3) = 0 for a differential equation is __________.