The ordinary differential equation dx⁄dt = -3x + 2,with x (0) = 1 is to be solved using the forward Euler method. The largest time step that can be used to solve the equation without making the numerical solution unstable is ________.
-
Solution
A sequence x[n] is specified as
\(\begin{bmatrix} x[n] \\ x[n-1] \end{bmatrix} =\begin{bmatrix} 1 & 1 \\ 1 & 0 \end{bmatrix}^{n}\begin{bmatrix} 1\\ 0 \end{bmatrix},for\: n\geq 2.\)The initial conditions are x[0] = 1, x[1] = 1, and x[n] = 0 for n < 0.The value of x[12] is ______
-
Solution
A signal 2cos(2π⁄3t) – cos(πt) is the input to an LTI system with the transfer function H(s) = e3 + e-3.
If Ck denotes the kth coefficient in the exponential Fourier series of the output signal, then C3 is equal to
-
Solution
If the vectors e1= (1, 0, 2), e2= (0, 1, 0) and e3= (–2, 0, 1) for man orthogonal basis of the threedimensional real space R3,then the vector u= (4, 3, – 3) R3 can be expressed as
-
Solution
The particular solution of the initial value problem given below is \(\frac{d^{2}y}{dx^{2}}+12\frac{dy}{dx}+36y=0\) with y(0) = 3 and \(\frac{dy}{dx}\mid _{x=0}=-36\)
-
Solution
A fluid (sp. gr = 0.9, μ- 1.2 Pa – S) flows in a laminar state between two stationary parallel plates set 3 cm apart. If the steady discharge is 500 cm3/sec per cm width of plates, the shear stress at a distance 1 cm from either boundary is
-
Solution
A applied couple ‘M’ is moving from A to B on a simply supported beam of span ‘l’ as shown in the given figure.Then which of the following statements are correct
1.maximum absolute bending moment will occur when couple is at the mid span.
2.maximum absolute bending moment will occur when couple is at either end.
3.minimum absolute bending moment will occur when couple is at the mid span.
4.minimum absolute bending moment will occur when couple is at either end.
-
Solution
For the given truss:-
Choose correct shape of ILD for member U2 L2(Take Tension positive)
-
Solution
A beam is made of two identical metal flats soldered together what is the ratio of stiffness of this beam to the stiffness of a beam in which the two flats are not soldered and which act independently?
-
Solution
A propped cantilever ABCD is loaded as shown in the figure.The collapse load for the beam AD is ____\(\frac{M_{p}}{L}\)
-
Solution