1. The free-fixed rod ( length of 2 m, diameter of 0.5 mm, density of 300 kg/m) vibrates in lengthwise direction(longitudinal vibration).(a) Determine the Young's modulus so that the first natural frequency is 500 Hz.(b) For this rod, calculate the second natural frequency.

Answered: Image /qna-images/answer/2ca5d7f6-990d-4937-988a-466c0e72e422.jpg

The free-fixed rod ( length of 2 m, diameter of 0.5 mm, density of 300 kg/m') vibrates in lengthwise dire ngitudinal vibration). Determine the Young's modulus so that the first natural frequency is 500 Hz.

The free-fixed rod ( length of 2 m, diameter of 0.5 mm, density of 300 kg/m') vibrates in lengthwise dire ngitudinal vibration). Determine the Young's modulus so that the first natural frequency is 500 Hz.

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: k2 m 2000000000- 2000000000 2000000000-

A: Given , f1= 5Hz f2 = 3.6 Hz

Q: Given the Vibration system with nmultiple degree o' freedom. For string 1, k1 = 10kN/m For string 2,…

A: Given Stiffness, k1 = 10 kN/m k2 = 20 kN/m k3 = 30 kN/m…

Q: 1.3 m- m- 1.5 k I = 0.6 k %3D

A: given:

Q: AD Point A is connected to a spring to maintain the bar in vertical direction, and th stiffness k =…

A: The mass of the uniform bar AB is given as,m=8 kg The length of the uniform bar AB is given as,…

Q: A 3 kg mass suspended from a spring having stiffness of k= 200N/m. if the block is pushed 50mm…

A: Let us draw the mass-spring system General solutions of that differential equation Hence the…

Q: 5(0); A shaft of 40-mm diameter and 2.5-m length has a mass of 15 kg per metre length. It is simply…

A: To find: The frequency of the transverse vibration. Given: The diameter of shaft is d=40 m. The…

Q: The system is in equilibrium in the position. Find the period of vibration for small amplitudes.…

A: Given data: k=75 N/mm=1.8 kg Need to determine the period of vibration for small amplitudes.

Q: The uniform beam is supported at its ends by two springs A and B, each having the same stiffness k.…

Q: 22–25. If the disk in Prob. 22-24 has a mass of 10 kg, determine the natural frequency of vibration.…

A: The mass of the disc is m=10 kg. The spring constant of the spring is k=80 N/m. The radius of the…

Q: 1. The free-fixed rod ( length of 2 m, diameter of 0.5 mm, density of 300 kg/m') vibrates in…

A: E – the material Young's modulus, I – the moment of inertia, ρ – the material density, A – the area…

Q: On loading it with goods weighing 520 kN on a truck, its spring gets compressed by 26 cm, The weight…

Q: While standing in an elevator, the man holds a pendulum which consists of an 18-in. cord and a…

A: Given data :m=0.5 lba=4 ft/s2l=18 ing=32.2 fts2→acceleration of pendulum=g-a=32.2-4=28.2 fts2

Q: A simply supported beam of square cross section 5 mm x 5 mm and length 1 m, carrying a mass of 2.3…

Q: ] Derive the differential equation of motion for the system shown; Determine th e of the steady…

A: Given- m=6kg k=8 KN/m c=40 N-s/m Y=80mm=0.08m ω=30 rad/sec

Q: A spring mass system has a mass of 5 kg and k = 100N/m is pulled down a distance of 100 mm from the…

A: Find the period of vibration , the static deflection at rest and the maximum velocity.

Q: A cas have M = 1000 kg, eppective stiptness of sPoing 200 kN/ if it is dõiven along Bough doad that…

A: The mass and stiffness of the car body is given Mass (m) =1000kg Stiffness (k)=200kN/m = 200000N/m…

Q: k = 200 N/m A rope is wrapped around a 5 kg uniform disc which is pinned at O. 2. No slipping occurs…

Q: Ql: A carriage is moving on a sinusoidal road as shown in the figure, the velocity of the carriage…

A: Given:Velocity of empty carriage,V=0.3msDamping factor=0.5Initial Amplitude,AO=20cm=0.2mLet…

Q: 22-49. The light elastic rod supports a 4-kg sphere. When an 18-N vertical force is applied to the…

A: Given, Mass (m) = 4 kg Froce (F) = 18 N Δy = 14 mm=0.014 δ0 = 15 mm Harmonic frequency (ω0 )= 2 Hz…

Q: above the other, and a mass of 10 kg is attached at the middle point of its length. Determine the…

A: Solution :- Given data :- F = 100 N δ = 10 mmm = 10 kg

Q: A 2-lb weight is suspended from a spring having a stiffness k = 2 lb/in. If the weight is pushed 1…

A: Given Data: The weight of object is W = 2 lb. Stiffness of spring is k = 2 lb/in. Initial…

Q: Determine the natural frequency of the spring- mass system in both radians per second and cycles per…

Q: A part of a machine has a reciprocating component which is simple harmonic, making a 200 complete…

Q: The homogeneous beam has a mass of 3m and supported at point B. For small oscillations, determine…

A: Solution : The kinetic energy of the system is given as:…

Q: A load W is supported by a beam of length I. Determine the spring constant and the frequency of free…

Q: QI/ A vertical shaft 100 mm in diameter and 1 m in length has its upper end fixed at the top. At the…

A: “Since you have asked multiple question, we will solve the first question for you. If you want any…

Q: A shaft of length 0.95 m supported simply at the ends, is carrying a body of mass 84 kg at 0.38 m…

A: Solution:

Q: 16. Evaluate the first two natural frequencies of the lateral vibration of the simply supported beam…

A: In lateral vibration the particles of beam move approximately perpendicular to the axis of the beam.…

Q: 3. The Department of Highways at Dale City put up a signage with a thickness of 4 inch at the corner…

Q: The mass of the car is 1400 kg, which is evenly distributed over the four springs. The car's own…

A: Given data: The mass of the car is m=1400 kg The deflection of the spring is x=20 cm=0.2 m

Q: Q2-A shaft of length 0.75 m, supported freely at the ends, is carrying a body of mass 90 kg at 0.25…

Q: A spring of negligible weight which stretches 1 inch under tension of 2 lb is fixed at one end and…

Q: When a 2-kg block is suspended from a spring, the block oscillates with a cyclic frequency of f = 45…

Q: A shaft of length 0.95 m supported simply at the ends, is carrying a body of mass 84 kg at 0.38 m…

A: Given data , l=0.95 m a = 0.38 m b = 0.57 m E = 200 GN/m2d=65mm

Q: Consider a mass-spring system with a mass of 1 kg attached to the spring, having spring constant 9…

A: given data;mass (m)=1kgspring constant k=9kg/mF(t)=4cosωt

Q: If the 20-kg wheel is displaced a small amount and released, determine the natural period of…

A: Vibration occurs when an elastic body, such as a spring, a beam, or a shaft, is moved from its…

Q: machine mounted on elastic supports, is free to vibrate vertically. The machine has a mass of 40 kg…

A: mass of machine, M=40kgunbalancing mass, m=2kgeccentricity, e=150mmResonance speed, Nn=621rpm…

Q: A spring is stretched 200 mm by a 15-kg block. If the block is displaced 100 mm downward from its…

A: The SHM equation is my..+ky=0The general solutions of the above differential…

Q: tatic deformation of a vertical rope of an elevator-cabin of mass m=300 [kg] is ðst= 0,6 [mm].…

A: This is problem in mechanical vibrations, we are to determine the natural frequency and the time…

Q: A shaft of length 0.95 m supported simply at the ends, is carrying a body of mass 84 kg at 0.38 m…

Q: The 30kg cylinder causes a static deflection of 50mm in the coiled spring. If the cylinder is…

Q: Determine the natural frequency of torsional vibrations in a shaft of diameter and length 100 mm and…

Q: Determine the natural period of vibration of the pendulum if it is given a small displacement and…

A: This is a physical pendulum

Q: When a 2-kg block is suspended from a spring, the spring is stretched a distance of 40 mm. Determine…

A: To find : The period of vibration for a 0.5 kg block attached for the same spring. Given : The…

Q: is the period of e same length o e density but ha -Corth

Concept explainers

Forced undamped vibrations

In mechanical engineering, vibration is expressed as the term that occurs due to an object's backward and forward movement about a point of equilibrium. Generally, there are three types of vibrations which are,

Question

1. The free-fixed rod ( length of 2 m, diameter of 0.5 mm, density of 300 kg/m) vibrates in lengthwise direction
(longitudinal vibration).
(a) Determine the Young's modulus so that the first natural frequency is 500 Hz.
(b) For this rod, calculate the second natural frequency.

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 with 2 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

An electrical switch gear is supported by a crane through a steel cable of length 4 m and diameter 0.01 m. If the natural time period of the axial vibration of the switch gear is found to be 0.01 s, find the mass of the switch gear. * 871 kg 1030 kg 1110 kg 955 kg
A motor that turns at 12,000 rpm is suspended from above by a single spring to isolate the building from its vibration. If the natural frequency of the system is to be one fourth of the vibration frequency, by how many centimeters should the spring extend be-yond its unloaded length when the motor is hung on it?
3. The 7.5 kg mass shown is vibrating freely with the following spring attached to it. If the required period of vibration is 0.35s, determine (a) the value of the spring stiffness constant R and (b) the vibration response with initial displacement and velocity of 5cm and 24 cm/s, respectively
Determine the velocity and frequency of vibration of a rope 6 m long with a mass of 2 kg and stretched with tension of 192 N.
A weight of 15N is vertical suspended by a spring of stiffness k=2N/mm determine natural frequency of free vibration of the weight
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 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 shaft of 50 mm diameter and 0.5m long is fixed at one end and other end carries a disc of mass 500 kg. The radius of gyration of the disc is 0.5 m. Find the frequency of torsional vibration, if the modulus of rigidity for the shaft material is 80 GN/m2 .
Question 3 A car with a mass of 1000 kg, has 4 suspensions, and has an un-damped natural frequency of vertical vibration of 5 Hz. Calculate: The stiffness of each spring The un-damped natural circular frequency of vertical vibration when the car is carrying five people each with a mass of 95 kg. The un-damped natural frequency of vertical vibration when the car is carrying five people each with a mass of 95 kg.
A spring-mass system K1, m, has a natural frequency of f1. If a second spring K2 is added in parallel with the first spring, the natural frequency is lowered to 1/2f1. Determine K2 in terms of K1.
mass 1 is excited by a harmonic force whose maximum value and frequency are 2 N and 50 Hz, respectively. Where m1 = 5 kg, m2 = 5 kg, k1 = 2000 N/m and k2 = 2000 N/m. Which answer represents the amplitude X1 and X2?
A system of beams supports a motor of mass 1200 kg. The motor has an unbalanced mass of 1 kg located at 6 cm radius. It is known that the resonance occurs at 2210 rpm. What amplitude of vibration can be expected at the motor’s operating speed of 1440 rpm, if the damping factor is assumed to be less than 0.1?