please help and clearly explain number 2. How would I find critical and underdamped? Question 2For the same differential equation as in Problem 1:* + 2a + 25 x25 v (t)Find the condition on a so that the zero-input response is overdamped.○a #0a> 5a > ν 25O a ≥ 25= Question 1dx (t)* (t)dtConsider the following differential equation:25 v (t)* + 2a + 25 x =9O Xz-i (s)x (0) = 5, * (0)Let the external input be zero. Write the Laplace transform of the zero-input-response xz-i (t),i.e., Xz-i (s) L{xi (t)} in terms of the given initial conditions and aO Xz-i (s)* (t)==(Note: All given initial conditions are just before t = 0, i.e.,x (0) x (0), * (0) * (0_ ) in all problems).==O Cannot be determined with the given information.O Xz-i (s)=d² x(t)dt²= - 2925with initial conditions:s²+2 as+25a 582 +2 as+255 (8+2a) - 29s2+2 as+25

Answered: Image /qna-images/answer/da9b5e59-ab49-4de3-a642-a864c640cf4f.jpg

Answered: For the same differential equation as…

For the same differential equation as in Problem 1: * + 2a + 25 x = 25 v (t) Find the condition on a so that the zero-input response is overdamped. 0 a 70 0a>5 Ο α Σ ν 25 O a ≥ 25

Introductory Circuit Analysis (13th Edition)

13th Edition

ISBN:9780133923605

Author:Robert L. Boylestad

Publisher:Robert L. Boylestad

Chapter1: Introduction

Section: Chapter Questions

Problem 1P: Visit your local library (at school or home) and describe the extent to which it provides literature...

See similar textbooks

Related questions

Q: This unity feedback system with the shown Bode plot is stable 50 Phase (deg); Magnitude (dB) 0 -50…

A: Given, Bode plot is We need determine the stability of the unity feedback system.

Q: For the network given in the following figure, Re is equal to RT Μ 9Ω Μ ΖΩ ΖΩ

A: We the given circuit , we need to find out the total resistance .

Q: 9) Coherent binary FSK modulation is used to transmit two equiprobable symbol waveforms s₁ (t) = A…

Q: Q1. The transfer function of a second order control system is Y(s) K C(s) S²+10S + K Suppose that…

Q: 2. True or false In general, the output O depends not only on the signal input I but on…

A: As per guidelines given to us we can only provide the solution of first question in multiple type of…

Q: Example 4.2: A communication source produce information in the form of encrypted data using three…

A: Given: Three symbols (L, M, N) and their probabilities, and conditional probabilities, To find:…

Q: d R₁ E4 E₁ www www R4 с a R₂ www w R3 E2 E3 b

A: Given data Voltage source; E1=20VE2=8VE3=4VE4=10V Resistance value; R1=5.3 ΩR2=9 ΩR3=2.6 Ω The…

Q: The biopotential is O a. Describes the transfer of information between cells O b. Electrical…

A: The bio potential is a electric potential that is measured between points in living cells. It…

Q: The circuit below has three resistors. If the potential of the battery is 10.0 V, what is the…

Q: a-Given W123 =W256, solve for x? b- A portion of music signal is sampled at 10M Khz and analyzed…

Q: The "moderate voltage limiting device" used in ECG circuitry is made of O a None of these Ob 2…

A: As per guidelines given to us we can only provide the solution of first question in multiple type of…

Q: Q1. Given the following block diagram, find the root locus transfer functions for gains K₁ and K₂.…

Q: 4-) Draw a pole-zero plot of the signal in the z-plane and explain the system stability and…

Q: Example 9.22 The resistance and standstill reactance of each phase of a 3-phase induction motor with…

Q: A 40-KVA, 3,300/240-V, 50 Hz, 1-phase transformer has 660 turns on the primary. Determine (a) the…

A: In this question We need to determine the unknown parameters. We know V1 /V2 = N1 /N2 Apparent…

Q: (i) Scenario A company manufacturing extra low voltage fluorescent fittings is looking at improving…

A: Given data Supply voltage/ primary voltage, Vprimary=230 V Secondary voltage, Vsecondary=24 V Choke…

Q: Q4: Calculate (1) the percentage ripple, (2) the regulation, and (3) the optimum number of stages…

A: (1) percentage ripple total number of capacitors for 12 stage cockroft walton type voltage…

Q: 2. [20% ] For each circuit in Figure2, determine the Thevenin equivalent as seen from terminals A…

Q: i(t) iR R iL 0000 ic A) 336.5 B) 300 C) 250 D) 223.6 E) 315.8

Q: Q4. a) As shown in Figure Q4.1, ten diodes are to be operated in series in a 5000V peak string…

A: Series operation of Switches:

Q: 6. A loop measuring 15 cm on a side has 50 square turns. When placed in a 0.75-T

Q: 24 R(s) 7 (5+3) (5+4) D(s) 8 s(s+2) C(s)

Q: Two metallic terminals protrude from a device. The terminal on the left is the positive reference…

Q: Find the center and vertices of the ellipse .4x^2+9y^2-24x72y+144=0

A: Given the equestion of ellipse 4x2+9y2-24x+72y+144=0

Q: Example: A 32/4 dipole is radiating into free-space. Input power to the dipole is 100 W. Assuming an…

Q: Obtain R(S) G₁ H₁ G₂ H₂ GA G₂ C(s)

Q: 11) A binary receiver system receives a bit rate of 1 Mbits/sec. The wavefoem amplitude is 5 mV and…

A: A binary receiver system receives a bit rate of 1 Mbits/sec. The wavefoem amplitude is 5 mV and the…

Q: Calculate the values of new currents in the circuit when the 2-ohm resistor is increase to 4 ohms

Q: QUESTION 1 At 1 pm, a bacterial culture weighted 100 grams. At 4.30 pm, it weighted 250 grams.…

Q: What of the following is not true about collisional ionization in gases? O a. Needs free electrons…

Q: Find the circular convolution of x[n]= 3 8[n]+ 28[n-1]-8[n-3] and h[n]=8[n]- 28[n-1]-3 8[n-2] +4…

A: Introduction Convolution: The relationship between an LTI system's input and output is expressed…

Q: 2. A horizontal magnetic field of 2 × 104 T forms an angle of 30° with a current-carrying wire, 0.8…

A: Given: Horizontal magnetic field: B=2×10-4T forms an angle θ=30° Length of wire L=0.8mCurrent I=15A…

Q: 1. (20 pts) For the circuit shown below, a. (10 pts) Use the node-voltage method to write the system…

Q: A lagging system with a complex load has a power factor of 0.75 and an applied voltage of 200V. if…

A: Given data, A lagging system has, Power factor cosϕ=0.75. Voltage, VL=200 V. Apparent power, S=10…

Q: A silicon PN junction employs ND = 5 × 1017 cm−3 and NA = 4 × 1016 cm−3 . (a) Determine the majority…

Q: Q5 On a common set of axes, plot the v-i characteristics for resistors R₁ = 4.7k²2, R₂ = 47k52, R₂ =…

A: Resistor The resistor is the behavior of the material or a substance due to which it tries to resist…

Q: The voltage ranges of the EEG Biopotential signals is from: Oa 10 µV to 100 mV O b. 10 pV to 100 μµV…

A: Option b 10µv to 100µv Explanation: Almost all of the- biopotentials including EEG, ECG, & EMG,…

Q: Here, we'll utilize a basic scenario to investigate the potential applications of the PN generator…

Q: 10) Consider a binary digital modulation system, where the carrier amplitude at the receiver is 1 V,…

Q: Find the Trigonometric Fourier Series of the given figure. Vm Vm/3+ T/3 2T/3 + T 2T

Q: Q-6 b, Consider a negative unity feedback system with forward path transfer function K G(s) = where…

A: Given- A negative unity feedback system with forward path transfer function. Gs=Ks+as-bs+c, To Find-…

Q: E=36 V I=1.3 mA+ 3. P= mW R=1kQ 5. P= /= 360 mA W R = 100 £2 E=24 V E=6V I= 4 mA 4. 1=__A P = 36 W…

Q: Q4. The electric field intensity of a plane wave propagating in a medium is given by: E = 10e ax…

Q: a) Determine the number of branches and nodes b) Find the delivered power from the source. -24 V…

A: In this question We need to determine the power delivered by the source. We know Power P = V2 /R

Q: Find the maximum power that can be delivered to the resistor R in the circuit shown.

A: In this question We need to determine the maximum power delivered to the resistance R. We know For…

Q: Draw the scheme of a high voltage fuse and list its basic components. Give short description of…

A: High Voltage Fuses are typically used in the power systems and are generally rated for the…

Q: What is characteristic impedance explain really simply?

A: Introduction Characteristic Impedance: In a transmission line, it is the most important parameter.…

Q: A long, straight wire carries a current of 15.0 A. What are the magnitudes of the magnetic field at…

A: Given that, I=15A We have to find B for a)r=2cm=0.02m b)r=4 cm=0.04m c)r=10cm=0.01m

Q: A.) A 25μC point charge is located at the origin, calculate the electric flux passing through a…

A: It is given that: Point charge(q)= 25 μC (located at origin) Radius of sphere(r)= 20 cm Bounded by θ…

Q: 1. A 60-cm long, straight wire conducts a current of 12 A directed out of the page. It experiences a…

Question

100%

please help and clearly explain number 2. How would I find critical and underdamped?

Question 2
For the same differential equation as in Problem 1:
* + 2a + 25 x
25 v (t)
Find the condition on a so that the zero-input response is overdamped.
○a #0
a> 5
a > ν 25
O a ≥ 25
=

Question 1
dx (t)
* (t)
dt
Consider the following differential equation:
25 v (t)
* + 2a + 25 x =
9
O Xz-i (s)
x (0) = 5, * (0)
Let the external input be zero. Write the Laplace transform of the zero-input-response xz-i (t),
i.e., Xz-i (s) L{xi (t)} in terms of the given initial conditions and a
O Xz-i (s)
* (t)
=
=
(Note: All given initial conditions are just before t = 0, i.e.,
x (0) x (0), * (0) * (0_ ) in all problems).
=
=
O Cannot be determined with the given information.
O Xz-i (s)
=
d² x(t)
dt²
= - 29
25
with initial conditions:
s²+2 as+25
a 5
82 +2 as+25
5 (8+2a) - 29
s2+2 as+25

Expert Solution

This question has been solved!

Explore an expertly crafted, step-by-step solution for a thorough understanding of key concepts.

SEE SOLUTION Check out a sample Q&A here

Step 1

VIEW

Step 2

VIEW

Step 3

VIEW

Step by step

Solved in 3 steps with 3 images

SEE SOLUTION Check out a sample Q&A here

Similar questions

Problem 5. Which gives the Laplace transforms of the given time-domain function? ln [(s + sqrt 2)/(s - sqrt 5)] ln [(s - sqrt 2)/(s + sqrt 5)] ln [(s - 2)/(s + 5)] ln [(s - sqrt 2)(s + sqrt 5)]
i)determine laplace transform of signal x(t) in fig q1(a) and state its region of convergence ii)determine laplace transform of e^3t x(t)
TRUE OR FALSE 1. The Laplace transform of two functions is equal. The functions are equal. 2. Laplace transform is a linear operator. 3. The transfer function is the ratio of the Laplace transform of the output variable to the Laplace transform of the input variable, with all initial conditions equal to zero. 4. L(f*g) = L(f).L(g). 5. Every function f(t) has a Laplace transform. 6. Taking the inverse Laplace transform gives us a function that is in the time domain. 7. Inverse Laplace transform is a linear operator. 8. The Laplace transform of the product of two functions is the product of the Laplace transforms of each given function. 9. If the denominator of a Laplace transform has degree 4, you should expect to find 4 items in the table to use for writing the transform as a sum of terms. 10. L(f(t)/t) = -F’(s). 11. L(3y+5w)=3∙L(y)+5∙L(w). 12. Daniel Bernoulli is the original author of Laplace Transform. 13. The Laplace transform of the sum of two functions is equal to the sum of the…
Consider the function, F(s) = 5/s(s2+3s+2) where F(s) is the Laplace transform of the function f(t). The initial value of f(t) is equal to ?
Determine the signal f(t) from its Laplace transform F(s) given as: F2(s) = s^2 − 4s + 3 / (s − 1)(s^3 + 3s^2 − 10s − 24)
Consider the function, F(s)= 5/s(s2+3s+2) where F(s) is the Laplace transform of the function f(t). The initial value of f(t) will be ?
Signals and Systems Determine the inverse Laplace transform of below function 1)H(s) = 7/(s2+9)
Suppose for the circuit shown, Idc=24 mA, R=625 Ω, L=25 mH, and C=25 nF. There is no energy stored in the circuit when the switch opens at t=0. 1. Find V(s), the Laplace transform of v(t). 2. Find v(t) by finding the inverse transform of the partial fraction expansion of V(s).
The dynamics of a system which has an input and output of the differential equation, d^2y(t)/dt + 3dy(t)/dt + 2y(t) = r(t), where the initial conditions are given as y(0) = 0, dy(t)/dt =0, r(t) =1, t>=0. Use Laplace transform to solve for the time response of the system, (ie solve for y(t), t>=0)
I need help with the question below Consider a causal linear-time invariant system described by the differential equation 2y′(t) + 6y(t) = x′(t) − 4x(t)1. Using Laplace transform technique, determine the zero-input response yz (t) if y(0−) = -3. Assume x(0−) and its higher order derivative in the vicinity of t = 0 to be zero.2. Using the Laplace transform technique, determine the zero-state response if x(t) = δ(t − π)
Please provide Handwritten answer. The first question: State the difference between the controller and the sensors Question 2: Find the Laplacian Transform for each of the following: A. f(t) = 20 B. f(t)=1-5 C. f(t) = 81 + 14 D. f(t) = cos 20t E. f (t) = 3t + sin 2t F. f(t) = 100+ 12 sin 2t + 20t The third question: Find the inverse Laplace transform of the following two functions: A. Y(s) = B. Y(s) =
a. laplace transform of DE b.simplified algebraic expression of the laplace transformation by equating it in terms of its dependent variable, (I(s)). c. inverse laplace transform of each factor of the denominator of the laplace algebraic expession by using the Heaviside Expansion Theorems. D. WRITE THE DIFFERENTIAL EQUATION, i(t), using HET( where; i(t)=i^1(t) +i^2(t)+i^3(t)...).