Q2\ Amass is suspended from a spring system as shown in fig. Determine the natural frequency of the system. Given: m=30kg K = 1000 N/m K2= 2000 K3 =4000 N/m %3D Q3\ the mass of a spring-mass-dashpot system is given an initial velocity 10W, , where 10W,is the undamped natural frequency of the system. Find the equation of motion for the system, when = 0.5. Q4\Find the natural frequency of the system shown in fig. Given: m=10 kg, K, = 2500 ,K2 = 1500 N/m K3= 2000 Nm. A(m)

Q2\ Amass is suspended from a spring system as shown in fig. Determine the natural frequency of the system. Given: m=30kg K = 1000 N/m K2= 2000 K3 =4000 N/m %3D Q3\ the mass of a spring-mass-dashpot system is given an initial velocity 10W, , where 10W,is the undamped natural frequency of the system. Find the equation of motion for the system, when = 0.5. Q4\Find the natural frequency of the system shown in fig. Given: m=10 kg, K, = 2500 ,K2 = 1500 N/m K3= 2000 Nm. A(m)

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: Consider a spring–mass–damper system with m = 80 kg, c = 15 kg/s, and k = 1500 N/m with an impulse…

A: Given Spring constant, k = 1500 N/m Mass, m = 80 kg Damping coefficient,…

Q: 1. Draw the free-body diagram of the systmes depicted below and derive the differential equation…

A: For system (a):For system (b):For system (c):

Q: . What is the energy stored in the spring if the spring iscompressed 0.5 m?

A: Given data mass = 40 kgspring constant = 3000 N/mCompressed length = 0.5 mWe have to find the energy…

Q: For given mass (m=10kg) and two springs systems k1=30 N/m and k2= 20N/m. Find the following 1.…

A: Given data as per the question k1=30 N/m k2= 20N/m

Q: Consider a spring–mass–damper system with m = 80 kg, c = 15 kg/s, and k = 1500 N/m with an impulse…

A: Given Spring constant, k = 1500 N/m Mass, m = 80 kg Damping…

Q: Piston (M=5kg) is driven when the fly wheel (r=0.1m, J=0.5kgm^2) moves the arm (L=0.2m,m=1kg). The…

A: Given: To find: Natural frequency

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: The nat. period of an undamped system is 3 s, but with a damping force that is proportional to the…

Q: The 4-kg cylinder is attached to a viscous damper and to the spring of stiffness k-800 N/m. Write…

A: Given data:- Mass of the block =4 kg spring of stiffness = 800 N/m. c=124 N.s/m c=80 N.s/m To…

Q: For the mass-damper system at right, the model in terms of velocity is mv + cv = f. The time…

A: Solution: Given Data: mv.+cv=fτ=mc To Find: Depend-ness of the time constant on the damping.

Q: 3. An undamped spring-mass system has a mass that weighs 48 lb and a spring constant 0.5 lb/in. The…

A: This question is related to the spring-mass system. The elastic vibration wherever there's no…

Q: A 25 kg mass is attached to a spring with spring constant 100 N/m. The mass is driven by an external…

Q: This problem is an example of critically damped harmonic motion. A mass m = 8 kg is attached to both…

Q: You have a prototype Slinky with a lump of coal at the end. This forms a damped spring-mass system.…

A: Here Given:- m=1 k=3 b=1

Q: The equation of motion for the following single-degree-of-freedom system can be represented as meë +…

A: For solution refer below images.

Q: When testing the landing gear unit of a space vehicle drop tests are carried out. Figure 2.17 is a…

Q: 4. Consider the system shown below. Let K-2 N/m, C- 2 kg/s, M = 1 kg, x(0)=-0.1 m, and v(0) = 1 m/s.…

A: The mass is .The spring constant is .The damping constant is .The intial condition are .

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

Q: The mass of the represented system is released under the initial conditions xo 0.1m and xo -5m/s…

A: Given : x0 = 0.1 m v0 = - 5 m/s To find: Response graph Time at x = -0.05 m

Q: A .6kg block is hung from a spring with a force constant of 25 N/m. Calculate the displacement of…

A: Data given - Mass of the block = 0.6 kg Force constant k = 25 N/m

Concept explainers

Free undamped vibrations

Whenever an object/system displaces in either side of its equilibrium position with the help of an external/internal means, then the object/system moves regularly or randomly on both sides of its equilibrium position. This motion is called vibration. Generally, there are three types of vibration: longitudinal vibration, transverse vibration, and torsional vibration.

Question

Q2\ Amass is suspended from a spring system as shown in
fig. Determine the natural frequency of the system. Given:
m=30kg
K1 = 1000 N/m
K,= 2000 K3 =4000 N/m
Q3\ the mass of a spring-mass-dashpot system is given an initial
velocity 10W„ . where 10W,is the undamped natural frequency of
the system. Find the equation of motion
for the system, when F = 0.5.
Q4\Find the natural frequency of the system shown in fig. Given:
m=10 kg, K, = 2500 , K,
= 1500 N/m K3= 2000 N/m-
ttt
A(m)

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 by step

Solved in 2 steps

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

3. A 100-pound weight is suspended from a vertical spring whose module is 100 pounds per foot. The weight is pulled downward 9 inches from its equilibrium position and released. Viscous fluid exerts 20 Ibs of force when the plunger moves through it at 0.5 ft/sec; 3.a What is the damping condition? Write the equation which describes the motion of the weights. Show graph. 3.b displacement 3.c velocity 3.d acceleration
A glider of mass 0.350 kg is placed on a frictionless, horizontal air track. One end of a horizontal spring is attached to the glider, and the other end is attached to the end of the track. When released, the glider oscillates in SHM with frequency 4.15 Hz. Find the period of the motion. Find the angular frequency of the motion. Find the force constant kk of the spring. Find the magnitude of the force that the spring exerts on the glider when the spring is stretched by 0.0200 m.
For the mechanical system shown, a- Find the equivalent mass, equivalent spring stiffness and equivalent damping coefficient when x (the displacement of the 2 kg block) is used as the generalized coordinate. b- Derive the equation of motion of the system in terms of equivalent system parameters (equivalent mass, equivalent spring stiffness and equivalent damping coefficient). 3000 N/m 2 kg 200 N.s/m /=0.04 kg-m² r = 10 cm 1000 N/m 1 kg I' 400 N.s/m ial
The motion of a spring-mass-damper system satisfies the initial value problem: (photo attached) 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/mand k/m so that the poles are placed at - 4 +/- 4 j ?
3
Consider the double mass/double spring system shown below. - click to expand. Both springs have spring constants k, and both masses have mass m; each spring is subject to a damping force of F friction We can write the resulting system of second-order DEs as a first-order system, w'(t) = Aw(t), with w = (x₁, x₁, x₂, x₂) T For values of k = 4, m = 1 and c = 21,2 = 0.5±3.2i, V₁ 23,4= - 0.5 ± 1.13i, V3 1, the resulting eigenvalues and eigenvectors of A are -0.039 0.248i 0.813 0.024 +0.153i -0.502 -0.134-0.302i' 0.409 -0.216 - 0.489i 0.661 and (a) Find a set of initial displacements x₁(0), x₂(0) that will lead to the fast mode of oscillation for this sytem. Assume that the initial velocities wil be zero. (x₁(0), x₂(0)) Enter your answer using angle braces, (and ). cx (friction proportional to velocity). (b) At what frequency will the masses be oscillating in this mode? Frequency = rad/s
6. A 1kg mass is attached to a spring (with spring constant k = 4 N/m), and the spring itself is attached to the ceiling. If you pull the mass down to stretch the spring past its equilibrium position, when you release the mass and observe its (vertical) position, it's said to undergo simple harmonic motion. AT REST MASS PULLED DOWN wwww Under certain initial conditions, the mass's vertical position (in metres) relative to its equilibrium position at time t, y(t), can be modelled by the equation y(t) = cos(2t) – sin(2t), (Note that y measures how much the spring has been stretched, so y = 1 indicates the mass is Im below its equilibrium position, whereas y = -1 indicates it is 1m above its equilibrium position.) (a) Find expressions for the mass's (vertical) velocity v(t) (relative to its equilibrium position) and the mass's (vertical) acceleration a(t) (relative to its equilibrium position). (b) Is the mass moving toward the ceiling or toward the floor at t= T? Justify your answer with…
damping, c Sliding Crate with Bumper Stop A crate of mass m enters a lubricated slide at a loading dock with a velocity v, to the right and an initial position x(0) = x, in the diagram shown above. The sliding motion is lubricated, characterized by a linear damping coefficient C. At a distance x = L the crate contacts a bumper stop characterized by a spring constant k and a damping coefficient c. Numerical values for the system parameters are: C = 8 N-s/m k = 1000 N/m m = 50 kg X = 0 Vo = 5 m/s L= 20 m Ca is to be experimentally determined in completing this assignment Bumper: Assignment 1) Given these parameters, determine the governing dynamic equation for the crate position. 2) Convert the governing equation to state variable form. This requires two first-order equations: a. dv/dt f:(x,v) b. dx/dt = f.(x,v) where f, is a function of the states, x and v. where f, is a different function of the states, x and v. Make two sets of the above equations, one each depending on whether there…
B/ Two massless springs with spring constants k1=100 and k2=150 are attached to mass of (m=20 kg) at A in parallel as shown in Fig (a). An identical pair of springs is attached to mass B in series as shown in Fig (b). Taking mA = mB = m, find and compare the natural frequencies ws and wp and (ws/wp) of the two systems. (b)
a string is attached to a mechanical vibrator, which has a frequency of 30Hx. the sttring is 3.0m long and has a linear density of .4 g/cm. the tension is varied by adding weights to teh string passing over the pully. What tension is needed to cause the string to resonate with the vibrator in four segments. assume that he points where the string meets the vibrator and the pulley are approx nodes.
Consider the dynamic system shown below. Rod Pulley Rc Rod Pulley RA = 10 cm PIB 1A The following parameters are given for the system: m₂ = 1 kg RA mg mc 2 kg RB Rc 20 cm m₂ = 3 kg R₂ = 30 cm k = 1200 N/m Note that pulleys A and B are constrained to move together and pulleys C and D are constrained to move together. Useful note... a. Obtain the characteristic equation(s) for this system. b. The applied force is removed. Then, pulley A/B is turned 2 degrees and released from rest. Find the system response.
An m-mass pendulum is connected to a spring with the spring constant k through the massless rope along I as in the picture. x, i k www point y =0 m The spring is then given a deviation of x, so it moves at a speed of x. Assume point y = 0 is parallel to the spring, so that the potential energy of the pendulum negative value. If the pendulum has a deviation of 0, specify: The system motion equation uses the Euler-Lagrange equation.