Prob. # 5] A spring-mass system, k, and m, has a natural frequency f1. If a second spring k2 is added in series with the first spring, the natural frequency is lowered to ½f1. Determine k2 in terms of k1.

Prob. # 5] A spring-mass system, k, and m, has a natural frequency f1. If a second spring k2 is added in series with the first spring, the natural frequency is lowered to ½f1. Determine k2 in terms of k1.

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: Express, as a function of t, the time interval needed for the amplitude of an oscillation to reduce…

A: As the amplitude of an oscillation is reducing, it has to be damped oscillation. In damped…

Q: spring-mass system with m = 0.01 Mg and k = 5 kN/m is subjected to a harmonic force of amplitude…

A: m = 0.01 Mg = 10000 g = 10 kg k = 5 kN/m = 5000 N/m F0 = 0.25 kN = 250 N X = 100 mm = 0.1 m ω0 = ?

Q: A mass-spring system oscillates on a frictionless horizontal surface in simple harmonic motion with…

A: Given: Amplititude (A)=0.1m

Q: Two identical circular cylinders of radius r and mass m each, are connected by a spring, as shown…

A: Given that ,

Q: A pendulum is suspended from the cusp of a cycloid cut in a rigid support (see Figure). The path…

Q: The static deflection of a spring under gravity, when a mass of 1 kg is suspended from it, is 3 mm.…

Q: 8) If the mass of a simple pendulum m and its length L are doubled, then the period of time will be…

Q: Prob. # 2] The mass (Figure P2), m = 0.4 kg, is suspended from two springs in series with stiffness…

A: Given data: m=0.4 kgk1=20 N/mk2=30 N/m Need to determine the circular frequency of the mass.

Q: Figure Q3(b) shows a uniform bar AB of mass = 8 kg hinged at point C. Point A is connected to a…

A: Given data: The spring constant is k=500 N/m The mass is m=8 kg The small angle is θ=3.5°…

Q: Figure Q1 shows two pendulum of masses m1 and m2 and length 1 and 12, coupled together with a spring…

A: given data: two pendulum mass m1&m2 stiffness of sping=k find frequencies f1&f2

Q: The barrel of a field gun weighs 1500 lb and is returned into firing position after recoil by a…

A: Understand that the system will return to its original position without oscillation when the system…

Q: Problem 2 A railroad car of masse 20000 kg travelling at a velocity v=10 m/s is stopped at the end…

Q: Consider a mass-and-spring system containing two masses m, = 1 and m2 = 1 whose displacement…

Q: *An elastic string of length 2L is tightly stretched between two rigid supports. At this .nidpoint,…

A: length of the string is 2L weight of the ball is W let the tension in the string be T

Q: In the shown figure, let m1 = 1 kg, m2 = 2 kg, kı = k3 = 100 N/m and k2 = 200 N/m. (a) Write the…

A: Consider a mass-spring system having two masses attached with three spring in the longitudinal…

Q: 4. Find the natural frequency of the system shown with and without the springs k1 and k2 in the…

A: Given data: stiffness=k1, k2 Need to determine the natural frequency with and without the springs.

Q: Two identical uniform bars are welded together at a right angle and are pivoted about a horizontal…

A: Data given - m = 27 kg l = 525 mm K = 616 N/m .

Q: In the system shown, a force P(t) is applied at C. Bar ABCD is of negligible mass. Determine: The…

Q: In the shown figure, let m1 = 1 kg, m2 = 2 kg, ki = k3 = 100 N/m and k2 = 200 N/m. (a) Write the…

A: Question (A) & (B) are solved here. For Question (C), Please post this question again.

Q: A block of mass m is suspended from two springs having a stiffness of k, and k2, arranged a)…

Q: for the system shown determine the natural frequency and the damping factor M1 a b M2 K M2 K

Q: A uniform disk with radius r and mass m can roll without slipping on a cylindrical surface and is…

A: Let's displaced the point 'A' by a small displacement 'x' which makes a small angle 'θ' at point…

Q: frequency given that W =1N, L0 =0.1m, b=0.15 m, and k = 80 N/m

A: Solution : Given data : W =1N, the free length L0 =0.1m, length of…

Q: The model shown is to be studied. Determine: Natural frequencies and Modes Obtain the response of…

A: FREE BODY DIAGRAM is a diagram of the system which represents all the forces acting on the system.…

Q: A small collar of mass 1 kg is rigidly attached to a 3-kg uniform rod of length L = 750 mm.…

A: FBD of pendulam is shown in figure.

Q: Q.4 A device to produce vibrations consists of the two counter-rotating wheels, each carrying an…

A: Given:- Relation of force transmitted by neglecting the damping. We get,…

Q: Two identical circular cylinders of radius r and mass m each, are connected by a spring, as shown…

Q: The system shown left composed by two rigid bars with a distributed mass of m and 2m, respectively.…

Q: Q5/ A machine of mass 75 kg are mounted on springs and is fitted with a dashpot to damp out…

A: Answer: (a) The resistance of the dashpot at unit velocity is 423.5 N/(m/s). (b) The ratio of the…

Q: A 4-lb uniform rod is supported by a pin at O and a spring at A and is connected to a dashpot at B.…

A: Given, k = 5 lb/ft c = 0.5 lb.s/ft AO = 6 in = 0.5 ft OB = 18 in = 1.5 ft OG = 6 in = 0.5 ft

Q: 4- The block is supported by the spring arrangement as shown. The block is moved vertically downward…

A: Since you have posted a question having multiple subparts. we will solve the first three subparts…

Q: A mass-spring system oscillates on a frictionless horizontal surface in simple harmonic motion with…

Q: A spring of stiffness 2 kN/m is suspended vertically and two equal masses of 4 kg each are attached…

A: Given: K , stiffness=2000N/m mass ,m=4kg find 1. Amplitude of vibration 2.…

Q: A machine weighing 1 kN is to be supported by 3 identical springs (Fig.). what is the stiffness of…

Q: m 1/4 L 3/4 L

Q: Large amplitude of vibration is experienced when an engine having mass (1500 + 2) kg operates at a…

A: A spring-mass damper system consists of mass nodes connected via springs and dampers arranged in a…

Q: In a single degree damped vibrating system a suspended mass of 8 kg makes 30 oscillations in 18…

Q: A 12-kg block is supported by the spring shown. If the block is moved vertically downward from its…

A: Given: The mass of block is m=12 kg. The spring constant is k=5 kN/m. The amplitude of motion is…

Q: · For the mechanical system shown determine: a) the equation of motion b) the natural frequency c)…

A: given; m=10kgI=0.1 kg-m2r=10cm=0.1mk=1.6*105N/mc=640N-s/m

Q: The figure shows a uniform rod with a mass of 3 kg and is pivoted at point A. There is a solid mass…

Concept explainers

Entropy

In physics, entropy means the amount of disorder or the degree of randomness associated with a thermodynamic system. The system is not self-organized when the entropy of the system is high. For instance, when a system is at an elevated temperature, its molecules are in random motion, vibrating and colliding with each other. During this scenario, the probability of finding a molecule at a particular place twice, is low. Under this circumstance, the system can be said to be in a high entropy.

Question

Answer with proper solution and correct. Thank you

Prob. # 5] A spring-mass system, kı and m, has a natural frequency
f1. If a second spring k2 is added in series with the first spring, the
natural frequency is lowered to %f1. Determine k2 in terms of k1.

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

A mass-spring system oscillates on a frictionless horizontal surface in simple harmonic motion with an amplitude A = 0.1 m. At what position (x = ?) would the kinetic energy of the system be equal to three times its elastic potential energy (K = 3U)?
Find the two natural frequencies of the system and describe its two natural modes of oscillation. See Attachment for assistance m1 = m2 = 1; k1 = 1, k2 = 2, k3 = 1
A uniform rigid mass of 2 lb is hinged at its centre and laterally supported at one end by a spring of constant k=300 N/m. If the equation obtained for frequency (ωn) in this system is ωn2 =k/m, what is the natural frequency?
The following mass-and-spring system has stiffness matrix K. For the mks values, find the two natural frequencies of the system and describe its two natural modes of oscillation. m1 m2 k1 k2 k3 x1 x2 K= −k1+k2 k2 k2 −k2+k3 m1=1, m2=5; k1=3, k2=10, k3=15 Let ω1<ω2be the two natural frequencies. ω1= ω2= (Type exact answers, using radicals as needed.)
A spring, with a 54 lb/in spring constant, is mounted on a vertical wall to support a 64.4 lb mass. At t=0 and an initial velocity of 9 in/sec. to the left, the mass is released from a position 2 inches to the right of the equilibrium position. Determine: a. Angular frequency
The system shown left composed by two rigid bars with a distributed mass of m and 2m, respectively. Determine the natural vibration period of the system. (k = 100 N/m,c = m = 10kg/m, L = 4m)
A machine tool with mass m = 1000 kg and mass moment of inertia J0 = 300 kg/m² rests on elastic supports, as shown in the figure. If the stiffnesses of the supports are given by k1 = 4000 N/mm and k2 = 3000 N/mm, and the supports are located at l1 = 0.4 m and l2 = 0.7 m, determine the natural frequencies and modal forms of the machine -tool.
The following vibration system oscillates with a small angle. x = 0.6m, y = 1.8m, k = 18N/m. From the motor: static deflection = 0.2m, forcing frequency = 30 rad/s. If the starting angle from rest is 2 radians (counter-clockwise) and mass A is 10 kilograms, determine: 1. The natural frequency in radians per second. 2. The natural period in second 3. The amplitude of free vibration in meters (reference: neutral position of the spring below), 4. The amplitude of steady-state vibration in meters (reference: neutral position of the spring below) 5. The magnification factor 6. The overall displacement in meters when t= 1 second (reference: neutral position of the spring below).
A mass of 36.3 kg is carried on an elastic system of stiffness 350 kN/m, and carries an absorber consisting of a mass 3.18 kg attached to it by a spring of stiffness 1 kN/m. Write down the equations of motion of the compound system and solve them to find the natural frequencies of the system and the corresponding amplitude ratios. [7.37 Hz; (X2/X1)= 39.8; 15.83 Hz; (X₂/X₁)= -0.2]
A machine tool with mass m = 1000 kg and mass moment of inertia J0 = 300 kg/m² rests on elastic supports, as shown in the figure. If the stiffnesses of the supports are given by k1 = 4000 N/mm and k2 = 3000 N/mm, and the supports are located at l1 = 0.4 m and l2 = 0.7 m, determine the natural frequencies and modal forms of the machine -tool. It's the same as this question but with different numbers:
ii. A mass spring system has three springs and mass m. Determine the equivalent spring stiffness, period and frequency of this system if the springs are connected in (a) series and (b) parallel. [Take the stiffness of the springs to be u, x and y and the equivalent stiffness as k]
4) Large amplitude of vibration is experienced when an engine having mass (1500 + 2) kg operates at a speed of 1500 rpm. An absorber having stiffness k2equal to 1500 N/m and mass m2 is attached to the primary system to absorb the vibration. Find: The magnitude of the mass of the absorber. The natural frequencies of the system after the addition of the absorber. The values of the stiffness k2 and mass m2 of the absorber in order to have the natural frequencies of the two degrees of freedom system 15% away from the forcing frequency.