The following data is given for the spring-mass-damper system shown in Figure 1: • K1 = 250 N/m, K; = 350 N/m • C1 =150 N/ (m/sec), C: = 200 N/ (m/sec) • m= (25 + 2) kg Detemine: i. The undamped natural frequency. ii. The damping ratio. The damped natural frequency.

The following data is given for the spring-mass-damper system shown in Figure 1: • K1 = 250 N/m, K; = 350 N/m • C1 =150 N/ (m/sec), C: = 200 N/ (m/sec) • m= (25 + 2) kg Detemine: i. The undamped natural frequency. ii. The damping ratio. The damped natural frequency.

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. Calculate the natural frequency and damping ratio for the system in figure below. Assume that no…

A: Natural frequency = 40.25 rad/sDamping ratio= 0.00158 System is underdampedExplanation:Step 1:…

Q: 1. For the system below: a. find the differential equation in terms of 0 (for small values of 0) b.…

A: Given:

Q: Solve the following second order spring–mass system and state whether the motion is…

A: The answer is given below.Explanation:Approach to solving the question: Detailed explanation:…

Q: 110% I DOP systems V. 1.1 Unsolved examples with answers Example 2.6 Calculate the torsional viscous…

Q: please find the soultion and explain will upvote if correct

A: Sure, The vibration at the natural frequency of the original system [1]. The system consists of two…

Q: eads damping force g force leads inertia and damping force are rce leads them by 90

Q: 5) The parameters for a one-degree-of-freedom system are M=10-kg. K=16- kN/m, and C=320-Ns/m. (a) By…

A: Given, Mass(m)= 10 kg Spring constant(k)= 16 kN/m Coefficient of damping(c)=…

Q: A certain mass-spring-damper system has the following equation of motion. x''+ cx' + 100x = f(t)…

Q: 0.08 0.06 0.04- 0.02 - x 2.13 Y: 0.002881 -0.02- x 0.45 Y: 0.03684 -0.04 2 2.5 时间:(s) 0.5 1 1.5 3…

Q: An aircraft undercarriage oleo can be simplified to a mass-spring damper system with a single degree…

A: Since you have posted a question with multiple sub parts, we will provide the solution only to the…

Q: 2. Consider a mechanical system consisting of two metal plates and two springs, connected vertically…

Q: PART A k = 2.000 N/m M=0.125kg A 0.125kg mass is attached to a horizontal spring of spring constant…

A: GIven: "Since you have not mentioned the part to be solved so we are solving the remaining…

Q: For small positive damping, c, in the sinusoidally forced mass-spring system mz" + cz' + kr = Ggcos…

Q: The undamped natural frequency. The damping ratio. The damped natural frequency.

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

The following data is given for the spring-mass-damper system shown in Figure 1:
• K1 = 250 N/m, K2 = 350 N/m
• C1 =150 N/ (m/sec), C; = 200 N/ (m/sec)
• m= (25 + 2) kg
Detemine:
i The undamped natural frequency.
ii. The damping ratio.
ii.
The damped natural frequency.
iv. Response of the system x (t)for given initial conditions:
xo = 0.005 m and vo = 5 m/sec.
x(t)
k
1
k
2
m
C1
C2
Figure 1

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 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

Mecjanical Vibration
Question is image. Only part i) ?
Q4\Find the type of damping in this system Where: m=5kg, K = 1500 /m N Damping coefficient= 1.5 *105 N-sec/m
4) Figure below shows a spring-mass- damper system. The mass is subjected to a steady force of P 2 N. The spring constant k 200 N/m, the mass m 5.2 kg and the damping ratio is f= 12.2 N. sec/m. What is the position of the mass after a sufficiently long time of force application? You may assume that the mass is initially at rest, and the spring at time t = 0 is in its unstretched condition. m k
QUESTION 15 A mass-spring damper system has the following parameters: • mass 250g damping constant 1/36000 Nh/m spring stiffness 500 N/m Calculate the damped frequency. O 1. Not possible to calculate. O 2.44.7 rad/s O 3.55.2 rad/s O 4.79.4 rad/s O 5. 25.8 rad/s
PARTS A & B solve carefully and label each part and CIRCLE FINAL ANSWER ( Use image Below) Part A - Assuming the elements are all linear, determine a model for the mass-spring-damper system. Make sure to clearly define the direction of positive velocity. Simplify your answer such that the model is in terms of the parameters (?, ?, ??, ??), the input force (?), the spring deflection and the mass velocity as well as their time derivatives. Part B - Take the ANSWER from PART A and replace the damping constant ? with the nonlinear expression ? = ?? + ?? + ? , with ? as the velocity of the mass.
The equation of motion of a certain mass-spring-damper system is 5x'' + cx' +10x = f(t). Suppose that f(t) = Fsin(wt). Define the magnitude ratio as M = X/F. Determine the natural frequency w_n, the peak frequency w_p, and the peak magnitude ratio M_p for damping ratio = 0.1 and the damping ratio = 0.3
A mass of 10kg oscillates at the end of a spring of stiffness, 5N/m. If the damping in the system is such that it gives a damping ratio of 0.45, determine. i) The critical damping. ii) The value of the damping coefficient. iii) The damped natural frequency. iv) The equation for the displacement if the initial velocity is 0.025m/s, and the initial displacement is 0 m.
part C and D
The quarter-car model of a vehicle suspension and its free body diagram are shown in Figure 1. In this simpliﬁed model, the masses of the wheel, tire, and axle are neglected, and the mass m represents one-fourth of the vehicle mass. The spring constant k models the elasticity of both the tire and the suspension spring. The damping constant c models the shock absorber. The equilibrium position of m when y=0 is x=0. The road surface displacement y(t) can be derived from the road surface profile and the car’s speed. Draw free body diagram (FBD) and derive the equation of motion of m with y(t) as the input, and obtain the transfer function. If assume: m=300 kg k=20000, 40000, 60000 N/m c=1000, 3000, 5000 N.s/m Plot magnification ratio vs frequency ratio (r=0-4) diagrams for the parameters given above (you can draw the three curves in one diagram for three different k values and do the same for the three c values as well). Use the derived transfer function to model the system and plot…
A pump of mass 30 kg is supported on a support structure which has 4 springsarranged in parallel with stiffness values of 10 kN/m, 15 kN/m, 8 kN/m and12 kN/m respectively. Viscous damping is present within the system and 1 kNs/mis applied by a damper.i) Produce a neat sketch of the system and state its equation of motion.ii) Determine the damping ratio for the system, commenting on its value. iii) Determine the damped frequency of vibration.iv) Determine the logarithmic decrement for the vibrating system.
3. A vibrating mass-spring system exhibits an acceleration amplitude of 27 mm/s² and a dis- placement amplitude of 2 mm. Compute the system's natural frequency.