Question 1: A uniform thin rod shown in Figure 1, nas a mass of 2 kg and carries a concentrated mass of 2.5 kg at B. The rod is hinged at A and is maintained in the horizontal position by a spring of stiffness 2 k N/m at C. Calculate the frequency of oscillation, neglecting the effect of the mass of the spring. 2.5 kg -300 mm 300 mm Figure 1: Uniform thin rod

Question 1: A uniform thin rod shown in Figure 1, nas a mass of 2 kg and carries a concentrated mass of 2.5 kg at B. The rod is hinged at A and is maintained in the horizontal position by a spring of stiffness 2 k N/m at C. Calculate the frequency of oscillation, neglecting the effect of the mass of the spring. 2.5 kg -300 mm 300 mm Figure 1: Uniform thin rod

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

Related questions

Q: 3) A one-degree-of-freedom system has an effective mass M-4-kg, an effective spring stiffness…

A: To find (a) The natural frequency ωn and critical damping ratio ζ (b) The response q as a function…

Q: mass ! hangs on the end of a cord around a pulley of radius 5 and moment of inertia 6, rotating with…

Q: (Uso Virtnal Work) Problem 7 In the system shown has mass m, length 1, and mass moment of inertia I…

A: The Answer is Below

Q: The period ra of damped linear oscillation for a certain 0.7 kg mass is 0.25 s. If the stiffness of…

Q: b. The semidefinite system shown in Figure 6 consists of a translating mass m=100 kg attached to a…

Q: A mass m = 4 kg is attached to both a spring with spring constant k = 197 N/m and a dash-pot with…

A: Mass of the system (m): 4 kgSpring constant (k): 197 N/mDamping coefficient (c): 4 N·s/mInitial…

Q: A spring hangs vertically from a bracket at its unweighted equilibrium length, as shown in the…

A: Given data as per question Spring constant , k=7.5 N/m, and the mass of the object,m=0.25 kg

Q: The period Ta of damped linear oscillation for a certain 1 kg mass is 0.27 s. If the stiffness of…

Q: X1 X2 m2 k1 k2

Q: PART A k = 2.000 N/m M=0.125kg A 0.125kg mass is attached to a horizontal spring of spring constant…

A: GIven: "Since you have not mentioned the part to be solved so we are solving the remaining…

Q: 5. For a simple seismograph as shown in Figure Q5 below, the co-ordinate X₁ measures horizontal…

A: Here, The mass m=1 kg. The spring stiffness k=10 Nm-1. The coefficient of the damper, c=2Nsm-1.…

Q: A horizontal spring is compressed by 15 mm when a force of 10 N is applied. A mass of 3 kg is…

A: Given:x = 15 mm = 0.015 mF = 10 Nm = 3 kg 1. a) Force constant:At the moment of compression, the…

Q: This problem is an example of critically damped harmonic motion. A mass m = 8 kg is attached to both…

Q: The elastic foundation of a heavy machine in Figure Q19 consists of elastic springs connected in…

A: Given data:- the springs have stiffness coefficient (k) = 10000 N/m The machine is of mass (m) =1164…

Q: The values of a, C, and bare > and , respectively.

Q: Use modal analysis to calculate the response of the drive train system of Problem 4.44 given by the…

A: Given : To find : Modal analysis

Q: 2. Figure 2 shows a simplified model to simulate a recording head flying over a rough disk surface…

A: a moving head in a recording head flying over a rough disk surface. The question asks you to derive…

Q: A .6kg block is hung from a spring with a force constant of 25 N/m. Calculate the displacement of…

A: Data given - Mass of the block = 0.6 kg Force constant k = 25 N/m

Q: Two identical thin bars, each of mass m and length L, are welded together at a right angle as shown…

A: Solution: Given Data: Displacement, xB=bsinωtStiffness = kLength =L The Equation of Motion of the…

Q: A machine, subject to a harmonic force of 500N with 0.5Hz frequency, is modelled as a mass of 800kg…

Q: For the mechanical system shown, a- Find the equivalent mass, equivalent spring stiffness and…

Question

Expert Solution

This question has been solved!

Explore an expertly crafted, step-by-step solution for a thorough understanding of key concepts.

This is a popular solution!

SEE SOLUTION Check out a sample Q&A here

Step 1

Step 2

Step 3

Answer:

Trending now

This is a popular solution!

Step by step

Solved in 4 steps with 2 images

SEE SOLUTION Check out a sample Q&A here

Knowledge Booster

Learn more about

Need a deep-dive on the concept behind this application? Look no further. Learn more about this topic, mechanical-engineering and related others by exploring similar questions and additional content below.

Similar questions

A thin cylindrical rod of uniform mass m and length L is suspended from the ends by two massless springs with constants k1 and k2 (Distance L1 and L2 on either side of the center of mass of the rod). The motion of the center of mass is constrained to move up and down parallel to the vertical y-axis. It also experiences rotational oscillations around an axis perpendicular to the rod and passing through the center of mass (I is the moment of inertia with respect to said axis). be y1 and y2 the displacements of the two ends from their equilibrium positions, as shown in Fig. a) Find the motion's equation (consider k1=k2=k)
QI Calculate the frequency of damped oscillation of the system shown in Figure () for the value m = 1.75 kg,c 350 N. s /m, k =7 x 107 N Am, a = 1.25 m and b = 2.5 m. If the mass pulled down 10' find the response of the system after cycle. I, mb² rigid link
For the system shown below, the disc of mass M rolls without slip. Assume that the mass M = 11 kg, the damping constant C - 209 Ns/kg and the stiffnesses K, = 9,036 N/m, K2 = 4,855 N/m, the radius of the disc R = 0.4 m and the moment of inertia of the disc about its centre I = MR² What is the damping ratio of the free vibration of this system? www K2 K1 M *No Slip
Consider the double mass/double spring system shown below. - click to expand. Both springs have spring constants k, and both masses have mass m; each spring is subject to a damping force of Ffriction -cz' (friction proportional to velocity). We can write the resulting system of second-order DEs as a first-order system, t' (t) = Au(t), with = (₁, 21, 22, 2₂) I For values of k = 4, m = 1 and c = 1, the resulting eigenvalues and eigenvectors of A are -0.039-0.248i 0.813 A₁2=-0.5±3.2i, v₁ = 0.024 +0.153i -0.502 -0.134-0.302i 0.409 -0.2160.489 0.661 (a) Find a set of initial displacements (0), 2(0) that will lead to the fast mode of oscillation for this sytem. Assume that the initial velocities wil be zero. A3,4 -0.5± 1.13i, z = and (2₁ (0), ₂(0)) = Enter your answer using angle braces, (and). (b) At what frequency will the masses be oscillating in this mode? Frequency rad/s
Q3/ For the system shown in figure if the damping ratio is 0.3 derive the equation of motion using Newton's second law and find: a- The natural frequency. b- The damping constant. c- The ratio of any consecutive cycles. k=2 x 10 N/m m = 4.2 kg 10 cm 40 cm 60 cm ITTTI
2. Consider the following compound pendulum, which consists of a thin rod attached to a pivot point 1/3 down its length, and has a thin disk of radius R attached to the end. Mass of the rod is m, and mass of the disk is me. Tasks: a. Find an Equation of Motion for rotational motion of the pendulum. Assume 0 <15° and apply the small angle approximation. b. Find the natural frequency w of this system. Report in terms of mr, ma, I, R, and g.
Refer to Figure Q2. A tray of mass mı is supported by 3 springs as shown in Figure 3(a). The natural frequency fa is 5.0Hz. An additional mass motor of m2 = 3.0kg (in OFF condition) is placed at the center on top of the mass, the natural frequency is observed to be 2.5Hz. a) Calculate the mass mı. The motor m2 is ON and it rotates at the speed of 600 rpm. Calculate: a) The transmissibility b) Attenuation c) Explain what will happen if the system run at Resonant Frequency m2 m1 Figure 2(a): Original system Figure 2(b): system with m2 added
The figure shows a bar of mass M-4 Kg and length L-1 m, has a concentrated mass at the end of the bar of m= 4 kg. The bar is supported by a pin at O and three springs as shown. In the value k- 800 N/m Find the natural frequency of the system. 2k O 17.0 rad/s O 14.4 rad/s O 10.9 rad/s 20.3 rad/s elle 00000 + 4 1 2 k > bar of mass M mass m
part b only please
assume there is damping in the system such that ζ=0.2
Derive the governing equation of motion of the mass-spring system on an inclined plane as shown in the figure below. Then determine the natural frequency of the given system. Please remember to state all assumptions and include a free-body diagram. ki ww k: m www A
The figure below shows the essential parts of a hydraulic brake system. The area of the piston in the master cylinder is 1.8 cm² and that of the piston in the brake cylinder is 6.4 cm2. The coefficient of friction between shoe and wheel drum is 0.50. If the wheel has a radius of 37 cm, determine the frictional torque about the axle when a force of 50 N is exerted on the brake pedal. N. m Wheel drum Pedal Shoe Master cylinder cylinder Brake