Q5(15 marks): Two equal pendulum free to rotate counterclockwise about the x-x axis are coupletogether by a rubber hose of torsional stiffness K lb.in/rad.as shown in Fig.5. determine the naturalfrequencies and mode shape for the normal modes of vibration. If L=19.3 in., W=3.86 lb, andk=20 lb.in/rad. Note: J=mL2X(1)m2mc²2X

From the question, we have the following parameters:Length of the pendulum, L = 19.3 inWeight of the…

Answered: Q5(15 marks): Two equal pendulum free…

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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Solve a,b,c and for c when the two dampers are connected to rigid bar (not parallel or series)
PART A k = 2.000 N/m M=0.125kg A 0.125kg mass is attached to a horizontal spring of spring constant k = 2 N/m and set into ocillation. Assume frictionless floor. 4 rod /s What is the angular frequency w of the vibration? o = How about the vibrating frequency f in Hz? f = 0.64 Hz. The position of the mass is given as x = A cos (ot + o). With your calculated value of w, fill in the following table (don't forget to set your calculator to "radian mode"). Each row represents a different oscillation with the same spring, pay attention to sign: v (m/s) .092 -.14 a (m/s²) 3076 -32 -.8712 -.64 A (m) t (s) x (m) -.02 F (N) .04 -.04 фо (rad) 0.03 2.5 0.3 - 212 1.36 0.04 0.02 0.2 0.06 .0545 0.1 0.4 .076 1.08 -. 08 0.04 0.3 |-26 - .25 2.94 -0.2 0.5 0.04 0.1 0.1 PART B Each of the rows in the following table represents an oscillation of a different spring and mass. Fill in the blanks. E is the total energy. Vmax, v, Xmax, and x are all positive in values. A (m) Vmax Xmax m (kg) k (N/m) E (J) x at…
QUESTION 19 The elastic foundation of a heavy machine in Figure Q19 consists of elastic springs connected in series and in parallel. Each of the springs has stiffness coefficient k = 10000 N-m-1. The machine is of mass m = 1164 kg and it is pulled by a distance 0.05 m from its equilibrium position and thereafter released from rest, such that simple harmonic oscillations occur. Determine the maximum acceleration of the machine. Provide only the numerical value (in m-s-2) to two decimal places and do not include the units in the answer box. m k Figure Q19: Elastic foundation of a heavy machine.
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Question 1: A) Plot the forced-undamped vibration response of a spring-mass system given by Eq. (3.13), page 265 of the Book, for the following sets of data: Set 1: 8st Set 2: 8st Set 3: 8st = 0.17 m, w = 6.1,wn = 7.6 r/s, x₁ = 0.11 m, x = 0.7 m/s = 0.17 m, w = = 0.17 m, w = 7.7,wn = 7.6½, x₁ = 0.11 m, x = 0.7 m/s Set 4: 8st = 0.17 m, w = 7.6 r/s, wn = 7.6 r/s, xo = 0.11 m, x₁ = 0.7 m/s 7.3 r/s, wn = 7.6 r/s, xo = 0.11 m, xo = 0.7 m/s x(t) = xo cos wnt + xo @n sin wnt + st B) Analyze and discuss the results. COS wt 1 cos @nt W Wn (3.13)
4. A student followed strictly correct procedure in the lab during the experiment of moment of inertia. He measured the mass and diameter of plastic cylinder with value of m = 0.36 kg and D = 0.1 m. The period of system without plastic cylinder is To = 0.667 s. The period of system with plastic cylinder T₁ = 0.92 s. Find: The spring constant K of the system. If a metallic cylinder and a plastic cylinder have same diameter and same thickness, which one has larger moment of inertia? Explain.
Deduce the expression for the free longitudinal vibration in terms of spring stiffness, its inertia effect and suspended mass. (b)A spring mass system has spring stiffness ‘s’ N/m and has a mass of ‘m’ kg. It has the natural frequency of vibration as 12Hz.An extra 2kg mass is coupled to ‘m’ and natural frequency reduces by 2Hz.Find the value of ‘s’ and ‘m’.
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Question 4 A thin disk is supported on spring-mounted bearings with vibration pickup and strobotac, as shown in Fig. Running at 800 rpm ccw, the original disk indicates a maximum amplitude of 2.90 mm at 45° cw from a reference mark on the disk o Next a trial weight of 3.0 oz is added at the rim in a position 91°cw from the reference mark and run at the same speed. If now the new unbalance is 6.0 mm at 80° cw from the reference mark, determine the position and weight necessary to balance the original disk o. رقم الاستار 459 30 35 Ret
A machine is supported on four steel springs. By neglecting damping, the natural frequency of vertical vibration the machine-spring system runs at f=200 cycles per minute. The machine generates a vertical force p(t)=posinot. When the machine runs at f₁ =30 cycle per minute the amplitude of vertical vibration is measured as u₁=0.2cm, at f₂=170 cycle per minute is u₂=1.042cm, and at f3-400 cycle per minute is u3=0.0248cm. Calculate the amplitude of vertical motion of the machine if the steel springs are replaced by four rubber isolators which provide the same stiffness, but introduce damping equivalent to -0.25 for the system. Evaluate the response of the system for frequency ratios r, respectively.
A machine with a mass of 250 kg is placed on isolator and the corresponding free vibration records is as shown in Figure. Determine the type of damping, its stiffness and damping constant. Consider the first 2 cycles. x(t) 0.01 0.008 0.006 0.004 0.002 0 -0.002 -0.004 -0.006 -0.008 -0.01 0 0.5 1 1.5 2 2.5 3 3 t 3.5

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