Problem 5: A helical spring of negligible mass is required to support a mass of50 kg. The stiffness of the spring is 60 kN/m. The spring and the mass system isdisplaced vertically by 20 mm below the equilibrium position and then released.Find: 1. the frequency of natural vibration of the system; 2. the velocity andacceleration of the mass when it is 10 mm below the rest position. [Ans. 5.5 Hz;0.6 m/s; 11.95 m/s²]

Answered: Image /qna-images/answer/5e683178-87db-4490-9589-b5adfb8bb4c5.jpg

Answered: Problem 5: A helical spring of…

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

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Problem (6) A 25 kg mass is resting on a spring of 4900 N/m and dashpot of 147 N-se/m in parallel. If a velocity of 0.10 m/sec is applied to the mass at the rest position, what will be its displacement from the equilibrium position at the end of first second?
Problem 6: An object of mass 2 kg is attached to a spring of stiffness 200 N/m on a horizontal frictionless surface. Then it is extending by 10 cm and then let free to oscillate. 1- How long will it take to make one complete oscillation? 2- Determine the amplitude and give an expression for the displacement as a function of time. 3- Calculate its displacement, velocity, acceleration and force acting on it after sec. 4- Calculate its velocity by the time it is extended by 0.5 cm.
A single-cylinder compressor with a mass of 150 kg is mounted on rubber wedges.Compressor rubber wedgesit has been observed that the wedges collapsed by 2mm when placed on it Damped free on wedges without starting the compressorwhen released into vibration, it completed 100 full oscillations in 10 seconds. The stroke of compressor is 100mm a-)Calculate the spring constant (k) of the wedges. b-) Calculate the degree of damping (c) of the wedges. c-)The vibration amplitude of the regular regime was measured as 1mm when the compressor was operated at a speed of 1000rpm In the compressorcalculate the amount of moving masses.
8. A spring of 21 cm length reaches 30.8 cm after hanging a mass of 1/4 kilogram on it. The medium through which the mass moves provides a damping force equal to three times the instantaneous velocity. Find the equation of motion if the mass is released from the equilibrium position with a downward velocity of 2 m/s. Calculate the time at which the mass reaches its extreme displacement, and what is the position of the mass at that moment? (Use g = 9.8 m/s²) Sol.
For the system shown below, the disc of mass M rolls without slipping. Assume that the mass M = 681.8627 kg and the stiffnesses K = 30338487.4491 N/m, K2 = 14293643.7357 N/m, the radius of disc R = 0.3164 m and moment of inertia of disc about its centre / = MR?/2. The natural frequency of the free vibration of this system is: K1 K2 * No Slip
with the aid of an engineering sketch of the mass and spring system, calculate the frequency of natural vibration of the dispenser
Problem 4: A part of a machine of mass 4.54 kg has a reciprocating motion which is simple harmonic in character. It makes 200 complete oscillations in 1 minute. Find: 1. the accelerating force upon it and its velocity when it is 75 mm, from mid-stroke; 2. the maximum accelerating force, and 3. the maximum velocity if its total stroke is 225 mm i.e. if the amplitude of vibration is 112.5 mm. [Ans. 149.5 N; 1.76 m/s; 224 N; 2.36 m/s]
A large industrial cooling system of mass 160 kg is supported by six springsarranged in parallel. Two of the springs have equal stiffness of 30 kN/m, twohave stiffness of 15 kN/m, and the remaining two have stiffness of 10 kN/m.Determine:i) the total stiffness of the spring system;ii) the natural frequency of vibration of the motor;iii) the periodic time for the vibration.
A set of scales consists of an instrumented spring from which the mass of the measured object can be deduced, and a damper to reduce oscillations of the readings. The mass of the scales is small and the damper is chosen to give critical damping when a 10-kg object is weighed. If a mass of 20 kg is placed on the scales, what is the damping ratio and how many cycles of vibration will occur before the reading on the scales settles to within 1% of the correct value?
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 k;equal to 1500 N/m and mass m; is attached to the primary system to absorb the vibration. Find: The magnitude of the mass of the absorber. ii. i. The natural frequencies of the system after the addition of the absorber. The values of the stiffness k; and mass m; of the absorber in order to have the natural frequencies of the two degrees of freedom system 15% away from the forcing frequency.
Consider a mass-spring system with a mass of 1 kg attached to the spring, having spring constant 9 kg/m. Assuming that the motion of the object is undamped, and the system is subjected to an external force F(t) = 4 cos ot, 6. a. Determine the displacement of the object if y(0) = 0, y(0) = 0. b. For what value of o the resonance would take place? a. [ y(t) = b. [ Resonance occurs at w = 3] ;(cos 3t- cos wt), w # 3; y(t) =t sin 3t, w = 3] w2-9
4. A mass-spring system exhibits a period of 5 s and a measured mass of 20 kg. Calculate the spring stiffness k.

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