A system is described by the differential equation
−5y′′(t)−3y′(t)+3y(t)=ys(t), Find the transfer function associated
with this...
A system is described by the differential equation
−5y′′(t)−3y′(t)+3y(t)=ys(t), Find the transfer function associated
with this system H(s). Write the solution as a single fraction in
s. H(s)=_______________?
A. Find a particular solution to the nonhomogeneous differential
equation y′′ + 4y′ + 5y = −15x
+ e-x
y =
B. Find a particular solution to
y′′ + 4y = 16sin(2t).
yp =
C. Find y as a function of x if
y′′′ − 10y′′ + 16y′ =
21ex,
y(0) = 15, y′(0) = 28,
y′′(0) = 17.
y(x) =
1. The differential equation y''+4y=f(t) and
y'(0)=y(0)=0
a. Find the transfer function and impulse response.
b. If f(t)=u(t)-u(t-1). Find the y(t) by convolution and Laplace
techniques. u(t) is unit step function.
c. If f(t)= cos(t) ; find the y(t) by convolution and Laplace
techniques.
2. The differential equation y''+3y'+2y=e^(-3t) and
y'(0)=y(0)=0
a. Find the system transfer function and impulse response.
b. Find the y(t) by convolution and Laplace techniques.
3. y''+3y'+2y=f(t) and
y'(0)=y(0)=0
Plot y(t) without any calculations and write...
Consider the linear time invariant system described by the
transfer function G(s) given below. Find the steady-state response
of this system for two cases: G(s) = X(s)/F(s) =
(s+2)/(3(s^2)+6s+24) when the input is f(t) = 5sin(2t) and f(t) =
5sin(2t) + 3sin(2sqrt(3)t)
3. ÿ+ 6ẏ + 5y = r̈+ 9r
(a) Find the system’s transfer function (b) Plot poles and zeros
on the s-plane (c) Provide the system’s time response from the
poles of the transfer function (d) Is the system stable? Why or why
not? (e) What type of system is it? (undamped, over damped,
critically damped, underdamped, etc.?)