The mass-spring-damper system when the mass is subjected to an externally applied force P(t)has the form of a square wave as shown in the figure below.10-10-| , 0

we know thatMd2xdt2=F-kx-RdxdtMd2xdt2+Rdxdt+kx=F…

Answered: The mass-spring-damper system when the…

The mass-spring-damper system when the mass is subjected to an externa nas the form of a square wave as shown in the figure below. PO 10 2r. 4x -10 0

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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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

The mass-spring-damper system when the mass is subjected to an externally applied force P(t)
has the form of a square wave as shown in the figure below.
10
-10-
| , 0<t<TI
In <t < 2n ° P(t + T) = P(t).
The force is described by (t) =
Give the value of A and the period T of the periodic function P(t).
Form the Fourier series expansion for P(t) by showing complete calculations of an, ao
and bn.
(a)
(b)

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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
S 4
2. Consider the spring mass damper system shown on the next page with m1 | m2 = 1 kg, k = 1 N/m, and b= 1 N/(ms). Note that you can neglect gravity by considering deviations from the system at rest. F(1) M m wwwww k
Pravinbhai
A) Show that for the damped spring – mass system , the peak amplitude occurs at a frequency ratio given by: ( 0 /@„) = /1– 2 7?
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Pleas give me step by step solution
QUESTION 3 Vibration absorber (also called tuned mass damper) is used to reduce* the vibration at the natural frequency of the original system. Consider a M-K system shown below. Original System x(t) Modified System x₁(1) X2(t) K K MA M 0000 M F(1) F(t) absorber K This system has a natural frequency at rad. The absorber mass and the spring are attached to the original system as shown in the figure, and the values are selected so that (1) the amplitude of the original mass, M. at the original natural frequency is zero, and (2) the new natural frequencies are moved away from the original natural frequency. The selection of absorber mass and stiffness, m and k, is easy. They have the same ratio as the ratio of the original system. That is, M/m = Klk. Find the transfer functions X1(s)/F(s) and X2(s)/F(s) before you can answer questions. What is the fundamental frequency (first natural frequency) of the modified system in rad/s? Use scientific notation with 3 signifincant figures. Omit…
answer would be appreciated thankyou
4- The logarithmic decrement can be obtained as & In*, is it possible to get a negative value of 8 when the system is damped (3 < 1)? Why?
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If the characteristic equation is system is stable or not stable. Stable Not stable s³ +8s² +21s +18 = 0 ,determine whether the 4