If u(t) = < sin(5t),
cos(5t), t > and
v(t) = < t, cos(5t),
sin(5t) >, use the formula below to find the given
derivative.
d/dt[ u(t) * v(t)] = u'(t) * v(t) + u(t)* v'(t)
d/dt [ u(t) x v(t)] = ?
Given a sinusoidal signal:
x(t) = Asin(2πft)
Find Fourier Transform (FT) of the sinusoidal x(t) given above
and plot the spectrum with:
a. A = 2, f = 1000Hz
b. A = 2, f = 9000Hz
c. A = 5, f = 1000Hz
d. A = 10, f = 10000Hz
A continuous signal contains the following two components:
x1(t) = 3 cos 20πt
x2(t) = 3 cos 50πt
(a) Find the minimum required sampling rate to avoid
aliasing.
(b) Draw the discrete time signals obtained after sampling, when
sampled with Fs = 100 Hz. Explain the disadvantage(s), if any, of
sampling beyond the Nyquist rate.
(c) Assume the sampling rate is Fs= 40 Hz, which components are
exposed to aliasing effects? Support your answer by showing
“Nyquist intervals” and the...
Consider the vector function given below.
r(t) =
2t, 3 cos(t), 3 sin(t)
(a) Find the unit tangent and unit normal vectors T(t) and
N(t).
T(t) =
N(t) =
(b) Use this formula to find the curvature.
κ(t) =
Given r(t)=ti+2sintj+2costk and u(t)=1/ti+2sintj+2costk, find
the following: 1. r(t) x u(t) 2. d/dt (r(t) x u(t) 3.now use
product rule for derivative of cross product of two vectors and
show same result
Given that Csc(x) = - 3 and Cos(x) < 0, find the exact
value of each of the trigonometric function of x.
Functions are: a. Sin(x) , b. Cos(x) , c. Tan(x) , d. Csc(x) ,
e. Sec(x) , f. Cot(x)