F(1) Spring m. Ball Dashpot Find the motion of the mass-spring system with the driving force F(t) shown above for the given data. [Hint: Read Forced Oscillations notes.] e-2t, 0 2 y(0) = 1, y'(0) =-1.5.

F(1) Spring m. Ball Dashpot Find the motion of the mass-spring system with the driving force F(t) shown above for the given data. [Hint: Read Forced Oscillations notes.] e-2t, 0 2 y(0) = 1, y'(0) =-1.5.

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: 3) A one-degree-of-freedom system has an effective mass M-4-kg, an effective spring stiffness…

A: To find (a) The natural frequency ωn and critical damping ratio ζ (b) The response q as a function…

Q: 5.) Consider the spring-mass-damper system with damping constant c, spring constant k, and external…

A: As per company policy, we are restricted to solve three sub-part of one question at a time. Please…

Q: O f =9f A block attached to a spring. oscillates on a frictionless horizontal surface with a period…

Q: mass ! hangs on the end of a cord around a pulley of radius 5 and moment of inertia 6, rotating with…

Q: Prob. # 3] A 0.453 kg mass is attached to a spring having static deflection of 7.87 mm. Calculate,…

A: Deflection (∆) =7mm To fund natural frequency of system

Q: 4. Consider the following spring-mass systems below with zero initial conditions described as x (0)…

A: Please find the below attached solution of problem given,feel free to ask any further…

Q: A 6-foot spring measures 7 feet long after a mass weighing 4 pounds is attached to it. The medium…

A: Given data, A 6 ft spring measures 7 ft distance when a weight 4 lb is attached. That means spring…

Q: Two springs, damper and a mass are attached to a rigid, weightless bar PQ as shown below. Write the…

A: The objective of the question is to derive the equation of motion for a system consisting of two…

Q: The elastic foundation of a heavy machine in Figure Q19 consists of elastic springs connected in…

A: Given data:- the springs have stiffness coefficient (k) = 10000 N/m The machine is of mass (m) =1164…

Q: Consider the damped harmonic oscillator shown below and modeled by the system: k - ()*+ (-) m (1)…

Q: A 100-kg tumbler produces a harmonic force of magnitude 5000 N. The stiffness coefficient of the…

A: Given, m = 100 kg F = 5000 N k = 10 x 104 N/m ζ=0.2X = 0.06 m

Q: 2. Figure 2 shows a simplified model to simulate a recording head flying over a rough disk surface…

A: a moving head in a recording head flying over a rough disk surface. The question asks you to derive…

Q: Q.2 Two springs, damper and a mass are attached to a rigid, weightless bar PQ as shown below. Write…

A: Two springs, damper and a mass are attached to a rigid, weightless PQ bar as shown below.Write the…

Q: A cam-follower system similar to that shown in Figure 3-15 (p. 103) has a mass m = 1 kg, a spring…

A: Given Mass, m = 1 kg Spring constant, k = 1 000 N/m Damping…

Q: Two identical thin bars, each of mass m and length L, are welded together at a right angle as shown…

A: Solution: Given Data: Displacement, xB=bsinωtStiffness = kLength =L The Equation of Motion of the…

Q: A 2 DOF mass-spring system shown below with n = 1, k = 8, and m = 2 with the initial conditions £₁…

A: From the given figure,

Concept explainers

Free Damped Vibrations

Free vibration is a type of vibration in which the external force is removed after giving the initial displacement to a body/system. In other words, in this type of vibration, force is applied at the initial displacement of the system, and after the initial displacement, force is removed, and the system vibrates at the natural frequency.

Question

F(1)
Spring
m.
Ball
Dashpot
Find the motion of the mass-spring system with the driving force F(t) shown above for the
given data. [Hint: Read Forced Oscillations notes.]
e-2t, 0<t<2
m = 1 kg, c =
4 Ns/m, k = 4N/m, F(t)
0,
t> 2
y(0) = 1, y'(0) =-1.5.

Expert Solution

This question has been solved!

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

This is a popular solution!

SEE SOLUTION Check out a sample Q&A here

Step 1

VIEW

Step 2

VIEW

Trending now

This is a popular solution!

Step by step

Solved in 2 steps with 1 images

SEE SOLUTION Check out a sample Q&A here

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

QI Calculate the frequency of damped oscillation of the system shown in Figure () for the value m = 1.75 kg,c 350 N. s /m, k =7 x 107 N Am, a = 1.25 m and b = 2.5 m. If the mass pulled down 10' find the response of the system after cycle. I, mb² rigid link
For the system shown below, the disc of mass M rolls without slip. Assume that the mass M = 11 kg, the damping constant C - 209 Ns/kg and the stiffnesses K, = 9,036 N/m, K2 = 4,855 N/m, the radius of the disc R = 0.4 m and the moment of inertia of the disc about its centre I = MR² What is the damping ratio of the free vibration of this system? www K2 K1 M *No Slip
Seen in Figure 1, a rotating mass (with mass moment of inertia Id to a fixed wall (on the far left) by a torsional spring (k 1kg* m² and angular position a) is attached 1Nm/rad) and a torsional damper. Consider the spring and damper as concentric and in parallel. Dampers with damping ratios of c = be considered. Att = 0.1, 0.5, 1.0, and 1.5kg * m²/s will 0, a unit step torque Tin is applied to the rotating mass. A unit step input is a forcing function whose value is 0 from -∞o to some time to and 1 from to to oo. Here, to = 0. Your tasks: k ww + C = la Od A Derive the equation of motion of the rotating mass. Write c as EOM's for the different values of c. Tin 0 Figure 1: Schematic of the mechanical system to model in Problem 1. em, you will solve part B over MA AB Grader Plea LO onment variable. You do not need to write separate ד ו. for
The motion of a spring-mass-damper system satisfies the initial value problem: d²x m- +bd + kx = F, x(0) = 0; *(0) =1 di? dt Given m = 1 kg, b= 5 Ns/m, k = 4 N/m, and F = 5 N. (a). What is the natural frequency of the system? (b). Is this system under damping or critical damping or over damping? Explain it. (c). Solve the given initial value problem. (d). The location of poles of X(s) affects the behavior of the system. How to choose parameters b/m and k/m so that the poles are placed at - 4+4j?
k 0.5m 1m The figure shows a slender rod with a mass of 6 kg. Attached to the rod is a spring of stiffness k = 250 N/m.Amoveable point mass m1 = 1 kg is position at a distance X from the pivot point. You can assume small angle oscillations from the equilibrium position shown in the figure. Calculate the required position, X, of the moveable point mass m1 needed to give the system a natural frequency of 5.3 rad/s. Give your answer to two decimal places.
Show this complete solution for this force driven without damping equation:
(note: for this problem do a hand calculation from t = 0 – 5 s , the rest use excel)
+ b 3. A tuning fork is an example of a "resonant system", that is, one that has a low damping ratio. A model of a (half) tuning fork is rod of mass m with air drag modeled as a damper connected approximately at its middle, and a torsional spring at the base of the cantilever. Assume the cantilever rotates back and forth about its pivot by a small angle o. Because other forces are much larger, you can reasonably neglect the effect of gravity in this model. The moment of inertia of a cantilevered beam pinned at one end is equal to ml2, where I is its length. (a) What is the natural frequency of this system if m= 0.1 kg and k = 2548 Nm/rad, and 1 = 0.1 m. Please give the value in rad/s and Hz. (b) Find an upper bound on the damping coefficient b that insures that the damping ratio of the tuning fork is no greater than = 0.01. (c) For this damping ratio, what is the damped natural frequency of the system? (d) For this damping ratio, what is the decay rate (the size of the exponent…
part b only please
The motion of a spring-mass system with damping is governed by: (see image) (a) Classify the damping as either undamped, underdamped, critically damped, or overdamped. (b) Find the general solution of the system and specify the amplitude, frequency and phase shift. (c) Solve the initial value problem
fd
0.5m 1m The figure shows a slender rod with a mass of 6 kg. Attached to the rod is a spring of stiffness k = 250 N /m .A moveable point mass m1= 1 kg is position at a distance x from the pivot point. You can assume small angle oscillations from the equilibrium position shown in the figure.