For the mechanical system shown, a force of 2 lb( step input) is applied to the system, the mass oscillates , as shown in fig. determine m, b, k of the system from this response curve. The displacement x is measured from the equilibrium position

For the mechanical system shown, a force of 2 lb( step input) is applied to the system, the mass oscillates , as shown in fig. determine m, b, k of the system from this response curve. The displacement x is measured from the equilibrium position

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

Similar questions

The spring-damper-mass system shown in Figure Q3(c) is at rest when strict bya hammer with an initial velocity of 0.4 m/s causing the mass to move upwards.Given that the mass m = 2 kg, spring constant k = 128 N/m and coefficient ofviscous damping c = 0.6 Ns/m.(i) Determine the damped frequency of the spring-damper-mass system.(ii) Base on the given conditions derived in Q3(c)(i) and parameters givenabove, describe how you would derive the equation of motion ofdamped-free vibration.
The equivalent mass of a SDOF of 10 kg. The system has a natural frequency of 80 rad/s. The system is at rest in equilibrium when it is subject to a time dependent force. Determine and plot the response of the system if it is subject to a force of (a) 10 sin(40t)N, (b) 10 sin(80t) N, and (c) 10 sin(82t) N.
(c) The spring-damper-mass system shown in Figure Q3(c) is at rest when strict by a hammer with an initial velocity of 0.4 m/s causing the mass to move upwards. Given that the mass m = 2 kg, spring constant k = 128 N/m and coefficient of viscous damping c = 0.6 Ns/m. (i) Determine the damped frequency of the spring-damper-mass system.
1 ) Derive a free body diagram with spring-mass-damper elements for given system. QUESTION 2 ) Derive equation of motion for given system in terms of m, c, k.
When a tree branch bends, it can be assumed that acts as a spring, i.e there is a restoring force −kx in response to a vertical deflection x. Internal friction of wood provides the dominant cushioning and is independent of the hanging mass, that is, F = −bẋ with b constant. We observe that a monkey of mass m1 hangs from the branch. East monkey oscillates many times, up and down before damping off appreciably, and coming to equilibrium. Then a second monkey of mass m2 hangs from the first monkey, and we observe that the monkeys together also oscillate several times before the branch reaches equilibrium. So the new equilibrium position of the branch is three times larger than with a single monkey. Besides, the energy loss per cycle for a monkey is half that of the loss with two monkeys. Based on these observations, determine the mass of each monkey (m1 and m2) in terms of a elastic constant k of the branch and a friction coefficient of the wood b. (Note: k and b are data)
Consider a spring-mass system with mass equal to 1 kg, spring constant equal to 25 Newton/meter.Which damping constant b causes critical damping?If the damping constant b in the above system is set to 3 N ∙ sec/m, then what can be said about the number of timesdoes the object pass through its equilibrium position?If the damping constant b in the above system is set to 8 N ∙ sec/m, then what is the interval of time between thesecond time the object returns to its equilibrium position and the third time it returns to its equilibrium position?
A mass of a 2 slug, when attached to a spring, causes an elongation of 2 ft in this spring and then comes to rest in the equilibrium position. Starting at t = 0 an external force equal to f(t) = 8 (sin (4t)) is applied to the system. Find the equation of motion if the surrounding medium offers a damping force equal to 8 times the instantaneous velocity.
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 vibrating system has the following parameters: m = 18 kg, K = 70 N / cm,c = 0.8 N.s / cm. Determine: a) The damping factor ξ, b) The frequency ofdamped oscillation ωD, c) the logarithmic decrease, d) the ratio of two amplitudes any consecutive and e) The equation of the general position X (t)
Considering that the displacement motion (x) of the single degree of freedom mass-spring-damper system given in the figure is measured from the static equilibrium position, draw the: a) free body diagram of the system. b) Derive the equation of motion. c) Find its natural frequency. d) When x (0) = 0.01 m is pulled down at t-0 and when x (0) = 0 m / s is released, its movement x (t) is m = 3 kg, b-12 N / m / s and Find it using the values of k = 120 N / m. e) Find the transfer function of the system when there is a force input of F = 10 N downward (in the + x direction) to the object. f) Show this transfer function with a block diagram.
Consider a vibrometer composed of a mass of m = 3.86 kg suspended from a spring of elastic constant k = 50 kg/m inside a box as shown in the figure. If placed above a machine that produces a vertical motion x(t) = 0.09sen3t m. Find the equation of motion of the system and the absolute amplitude of the mass in its steady state.
A block-spring system has a maximum restoring force Fmax = 0.1 N. If the amplitude of the motion is A = 0.01 m and the mass of the block is m = 100 g then the angular frequency w is equal to