1. A thin disk attached to the end of an elastic beam has three uncoupled modes of vibration. The longitudinal motion, transverse motion and the torsional oscillations are all kinematically independent. Calculate the following for the system shown. a. Longitudinal stiffness b. Transverse stiffness c. Torsional stiffness 65 cm I r=10 mm E-200 x 10° N/m² G=80 x 10° N/m²

1. A thin disk attached to the end of an elastic beam has three uncoupled modes of vibration. The longitudinal motion, transverse motion and the torsional oscillations are all kinematically independent. Calculate the following for the system shown. a. Longitudinal stiffness b. Transverse stiffness c. Torsional stiffness 65 cm I r=10 mm E-200 x 10° N/m² G=80 x 10° N/m²

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

(a) Calculate the natural frequency of vibration of a torsional pendulum as shown in figure task 2a with following dimensions Length of the rod l= 1m Diameter of the rod d= 5mm Diameter of the rotor D=_cm Weight of the rotor W=_kg The modulus of rigidity for the material of the rod may be assumed to be 0.85x 106 kg/cm? Kt
1. A .6kg block is hung from a spring with a force constant of 25 N/m. Calculate the displacement of the spring from its equilibrium length, assuming it is hung vertically and neglecting the spring mass. 2. The mass in (1.) is pulled downward by an additional 6 cm and held steady. Calculate the potential energy input corresponding to this additional displacement. 3. Calculate the period of oscillation of the mass/spring system once the object is released. 4. Write an expression for the vertical motion of the system, along the y (vertical) axis, in the form: ?(?) = ? cos(?t) (Use the appropriate values of A and ω in your expression). 5. Calculate the maximum speed of the oscillating object and its maximum kinetic energy. Do your results make sense based off what you got in 2? (I posted all 5 parts but could you answer only 4 and 5? Thank you!)
1. Mass suspended simple harmonic motion (measured from equilibrium position), displacement, velocity, and acceleration are x = 75mm, 450 mm/s, a = -442.5 mm/s^2. Period of Vibration and the amplitude of motion. 2. A uniform of rod of mass m = 3kg is supported by a pin at its midpoint c and is attached to a spring constant k = 120 N/m. If end A is given a small displacement, and released, determine the T of it resulting motion A k = 120 N/m = 3kg m = B
Figure Q3(b) shows a uniform bar AB of mass = 8 kg hinged at point C.Point A is connected to a spring to maintain the bar in vertical direction, and the stiffness k = 500 N/m. If point A is displaced counter-clockwise by a small angle θ = 3.5 degree and released, With the free body diagram and kinetic diagram, determine the initialhorizontal displacement of A. Then determine the period of vibration, the maximum velocity and acceleration at point A. p.s. This question was previously answered but because the solution images were unable to view I need to re-ask this question
Figure Q3(b) shows a uniform bar AB of mass = 8 kg hinged at point C.Point A is connected to a spring to maintain the bar in vertical direction, and the stiffness k = 500 N/m. If point A is displaced counter-clockwise by a small angle θ = 3.5 degree and released, With the free body diagram and kinetic diagram, determine the initialhorizontal displacement of A. Then determine the period of vibration, the maximum velocity and acceleration at point A.
S.3 The figure shows the fire extinguisher coppit. Basket and the weight of the fireman Find the vertical vibration natural frequency of the 2200 N COrpit. E= 2.1x1011 N/m²_L1=L2= L;= 3 m A1= 25 cm? A2= 15 cm? A;=8 cm? Bucket -Telescoping arm 12, Az 4, A1´ 45° FOT (a) 'oi (b)
2.20. Calculate the frequency of damped oscillation of the system shown in Fig. 2.23 for the values m=1,750 kg, c =3,500 N - s/m, k =7x 10° N/m, a= 1.25 m and b=2.5 m. Determine the value of the critical damping. rigid link k a FIGURE 2.23 Mass supported by a spring and dashpot through a rigid bar
Shock absorber. What is the smallest value of the damping constant of a shock absorber in the suspen- sion of a wheel of a car (consisting of a spring and an absorber) that will provide (theoretically) an oscillation- free ride if the mass of the car is 2000 kg and the spring constant equals 4500 kg/sec²?
A single degree of freedom mass-spring-damper system is subject to vibration under the influence of a harmonic force. On my site, it is given as m=2 kg, k=800 N/m, c=64 Ns/m. The amplitude of the harmonic force is F0=256 N and its frequency is w= 20 rad/s. Answer the questions in options a, b, and c according to the given information. 1) Calculate the damping ratio of the system (ξ) a.1 b.0.7 c.0.9 d.0.8 2)Calculate the magnification factor (M) of the system. a.0.86 b.1.25 c.0.312 D.0.625 3-) Calculate the maximum vibration amplitude (X) (meters). a.0.2 b.0.1 c.0.4 D.0.3
Exercise The figure below shows a cable-suspended rigid beam. The beam carries a box that may slide relative to the beam when it vibrates and rotates 0 (t) about its center of gravity, c. Write the equations of motion of the system. You may use Lagrange's equations or any other equivalent method. Solve the equations of motion assuming the free vibration case. Cables. m k k2 J, mj k1 k1 uw Lwww
4. Select the best statement to represent Free Vibration of Undamped System * A system that is left oscillate on its own without external force A system that is oscillating when a driving force is applied to the system periodically A system with having no energy lost during oscillation A system with having energy lost during oscillation
(1) A rigid bar (OA)with mass m and length L is simply supported at one end and free at the other end .A lumped mass M fixed at the end of A is subjected to a vertical harmonic excitation f(t). Two springs(k) are connected at the length a and b of the bar. Please calculate the natural frequency w and response vibration of the system. (Figure 1) Note: m=10kg, L=1 m, a=0.25m, b=0.5m, k=5000N/m, M=50kg, f(t)=Fcos2t (F=500N, Q=1000rpm). The vibration is very small. a b k L MA m M Figure 1: Single Degree Vibration System f(t) A X