Activity 1: The motion equation of damped mass-spring system as shown in Fig. 1 below is given as follows: m d²x dx +c. + kx = f(t),t> 0 dt² dt where: x(t): displacement in meters. m: mass in kg. c: damping coefficient in kg/s. k: spring stiffness constant in N/m. t: time in seconds. f(t): external force applied on system in N. k f(t) m [c C X(t) Fig. 1: Damped mass-spring system. Assume that: m = 2 kg, c = 3 kg/s, k = 20 N/m. Initially, assume ƒ (t) = 0. (1-a) Determine the general solution of x (t). (1-b) Given the initial conditions x (0) = 4, and x'(0) = 1, determine the particular solution of x(t). (1-c) Use Laplace transform to solve the given differential equation with the same initial conditions given in (1-b). (1-d) Critically evaluate how your mathematical solution behaves in transient and steady state regions. (1-e) Build a Simulink block model of the system, and generate the results of the differential equation. Show the model and the results in your report and specify the transient and steady state regions. Make sure you submit the simulation file (properly named). (1-f) Assume now that the external force f(t) equals 10 N, repeat all parts (1-a,b,c,d,e).

Activity 1: The motion equation of damped mass-spring system as shown in Fig. 1 below is given as follows: m d²x dx +c. + kx = f(t),t> 0 dt² dt where: x(t): displacement in meters. m: mass in kg. c: damping coefficient in kg/s. k: spring stiffness constant in N/m. t: time in seconds. f(t): external force applied on system in N. k f(t) m [c C X(t) Fig. 1: Damped mass-spring system. Assume that: m = 2 kg, c = 3 kg/s, k = 20 N/m. Initially, assume ƒ (t) = 0. (1-a) Determine the general solution of x (t). (1-b) Given the initial conditions x (0) = 4, and x'(0) = 1, determine the particular solution of x(t). (1-c) Use Laplace transform to solve the given differential equation with the same initial conditions given in (1-b). (1-d) Critically evaluate how your mathematical solution behaves in transient and steady state regions. (1-e) Build a Simulink block model of the system, and generate the results of the differential equation. Show the model and the results in your report and specify the transient and steady state regions. Make sure you submit the simulation file (properly named). (1-f) Assume now that the external force f(t) equals 10 N, repeat all parts (1-a,b,c,d,e).

Elements Of Electromagnetics

7th Edition

ISBN:9780190698614

Author:Sadiku, Matthew N. O.

Publisher:Sadiku, Matthew N. O.

ChapterMA: Math Assessment

Section: Chapter Questions

Problem 1.1MA

See similar textbooks

Related questions

Q: A motor operates at 1800 RPM and expends 2 HP. How many ft-lbs of torque does it provide at that…

A: Given data: The speed of the motor is; N=1800 RPM. The power of the motor is; P=2 HP.

Q: The traffic light hangs from the cables as shown. Draw a free-body diagram on a coordinate plane for…

A: Given data Weight of light =200N Draw the free body diagram

Q: D Question 2 Express the force TBC as a vector (in terms of i, j, k). Show all calculations on your…

A: Express the force TBC as a vector (in terms of i, j, k). Show all calculations on your paper and…

Q: Determine the magnitude of the resultant force. Express your answer to three significant figures and…

A: Data given- F = 44 lb

Q: A pneumatic system operating at 85 psi comprises a series of pneumatic actuators which consume 2.4…

A: Original CFM = 2.4 CFMOriginal pressure= 85 psiNew pressure= 120 psiAtmospheric pressure= 14.7 psi

Q: 0.2 m B 0.2 m 1.3 m 0.7 m A P Circular

Q: y F1 = 30 N 3 4 F3 = 50 N 20° F2 = 20 N

A: From the data given in question, F1 = 30 N F2 = 20 N F3 = 50 N

Q: Help , Handwritten only. No Chatgpt

Q: Phi = 40 degrees Theta = 35 degrees F1 = 425 Newtons Alpha = 60 degrees Beta = 45 degrees F2 = 625…

A: Given, ϕ=40°θ=35°F1=425Nα=60°β=45°F2=625N

Q: 2 ft 2 ft 3 ft A 6 ft

Q: 1-23.Determine the length of side C of the triangle shown in Figure P1-23.

Q: 100 lb 800 lb · ft A |C B 5 ft 5 ft

Q: F3 = 750 N 45° 5 30° F2 = 625 N F = 850 N

Q: 4. Use F₁ =3, 6₁ = 2, k₁₂₁ = 4₁ K3 = 2,63 = 1, J₁ = 2₁ J₂=5, find the impulse and step response of…

A: Given: To find: Impulse and step response

Q: Determine the x, y, z components of reaction at the thrust bearing D 0 = 0°.

Q: An object having 15 kg mass weighs 14 kg on a spring balance. The value of ‘g ‘at this place 14 m/s2…

A: mass = 15kg weight on spring balance = 14 kg

Q: 1-8. Determine angles a, b, and c (Figure P1-8). a 35° FIGURE P1-8

Q: 1- One millivolt is one millionth of a volt. (a) True (b) False

Q: 00 Ib, 120° 60°

Q: Determine the reactions at supports including the forces in the internal hinges (if any). Show all…

Q: - 2- 45 100lbs/ft 300lb 30 200lbs

Q: What is the worst-case distance between the bottom surface of the slot and the bottom surface of the…

A: Worst case between the bottom surface of the slot and the bottom surface of the part is the…

Question

1-c and 1-f

Activity 1:
The motion equation of damped mass-spring system as shown in Fig. 1 below is given as
follows:
m
d²x
dx
-+c+kx = f(t), t> 0
dt² dt
where:
x(t): displacement in meters.
m: mass in kg.
c: damping coefficient in kg/s.
k: spring stiffness constant in N/m.
t: time in seconds.
f(t): external force applied on system in N.
k
f(t)
m
C
Assume that: m = 2 kg, c = 3 kg/s, k = 20 N/m. Initially, assume f(t) = 0.
X(t)
Fig. 1: Damped mass-spring system.
(1-a) Determine the general solution of x (t).
(1-b) Given the initial conditions x (0) = 4, and x'(0) = 1, determine the particular solution of
x(t).
(1-c) Use Laplace transform to solve the given differential equation with the same initial
conditions given in (1-b).
(1-d) Critically evaluate how your mathematical solution behaves in transient and steady state
regions.
(1-e) Build a Simulink block model of the system, and generate the results of the differential
equation. Show the model and the results in your report and specify the transient and
steady state regions. Make sure you submit the simulation file (properly named).
(1-f) Assume now that the external force f(t) equals 10 N, repeat all parts (1-a,b,c,d,e).

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: Given details

VIEW

Step 2: part 1-a

VIEW

Step 3: part 1-b

VIEW

Step 4: Part 1-c and 1-d

VIEW

Step 5: Part 1-e

VIEW

Solution

VIEW

Step by step

Solved in 6 steps with 8 images

SEE SOLUTION Check out a sample Q&A here

Follow-up Questions

Read through expert solutions to related follow-up questions below.

Follow-up Question

slove f

Solution

by Bartleby Expert

SEE SOLUTION

Knowledge Booster

Learn more about

Need a deep-dive on the concept behind this application? Look no further. Learn more about this topic, mechanical-engineering and related others by exploring similar questions and additional content below.

Similar questions

mmetri Each part has a constant thickness with values indicated. 2.0 mm 1.5 mm 3.0 mm 2.0 mm A shear force, S₂ is applied. This results in shear flow, shown with red arrows, which has the following values: • Shear flow in part 13, just before point 3 - 38 N/mm Shear flow in part 23, just before point 3 = 44 N/mm Shear flow in part 43, just before point 3- 44 N/mm What is the shear stress in part 35, just below point 3? Express your answer in MPa, to 2 decimal places but without the units included. You have a 3% margin of error.
Determine the x, y, z components of reaction at the journal bearing C if 0 = 0°.
Express: 50000mm3 as m3 3.5m3 as mm3 20m3 as cm3 45cm3 as m3
Please do this carefully.
Pls help with questions no.24
The attached answer was provided for the attached question. The equation uses the given temperature in celcius and the answer is also given in celcius. The temperature was used in the equation without converting from F and the answer was supposed to be in F. I am worried that even if I converted the answer to celcius that it would be correct because temperature was used in the equation using the incorrect unit.
1.Impulse of a force is the integral of the force with respect to time over the time the force is applied. Impulse of a force is the integral of the force with respect to time over the time the force is applied. True False
Please look at the images for details about the question and the needed diagram. Make sure to include 2 places after the decimal point.
Two kinds of stress on a rod are tensile stress and compressional stress and the stress is calculated as the change in length over the total length. True True False
The horizontal component of Force F1 (unit is in N), H1= The vertical component of Force F1 (unit is in N), V1 = The horizontal component of Force F2 (unit is in N), H2= The vertical component of Force F2 (unit is in N), V2 = The horizontal component of Force F3 (unit is in N), H3= The vertical component of Force F3 (unit is in N), V3 = The vertical component of Force F4 (unit is in N), V4 = The horizontal component of Force F5 (unit is in N), H5= The vertical component of Force F5 (unit is in N), V5 = The horizontal component of Force F6 (unit is in N), H6= The vertical component of Force F6 (unit is in N), V6 = The sum of horizontal force component for the given system (unit is in N),begin inline style sum for H of end style = The sum of vertical force component for the given system (unit is in N),begin inline style sum for V of end style = The resultant of the given force system is (unit in N), R = The direction of Resultant Force is = Short Answer question
F3 = 52 lb 13 12 F1 = 80 lb 25°
F, = 50 N F2 = = 40 N -5 45° F1 = 20 N