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 0 = 3.5 degree and released, (i) With the free body diagram and kinetic diagram, determine the initial horizontal displacement of A. (ii) Determine the period of vibration. (iii) Determine the maximum velocity and acceleration at point A.

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 0 = 3.5 degree and released, (i) With the free body diagram and kinetic diagram, determine the initial horizontal displacement of A. (ii) Determine the period of vibration. (iii) Determine the maximum velocity and acceleration at point A.

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: Consider the system shown in the following figure, which is pivoted at point O. Suppose the system…

A: Given:- Moment about pin: ∑M = 0ftb = Mb2+mb23θ.. +cb2θ. +ka2θ…

Q: 1.2Kg is on a plane inclined at 30 degrees for which uc = 0.11. The block is connected to a spring…

Q: . What is the energy stored in the spring if the spring iscompressed 0.5 m?

A: Given data mass = 40 kgspring constant = 3000 N/mCompressed length = 0.5 mWe have to find the energy…

Q: A block of mass m hangs from the end of bar AB that is 8 meters long and connected to the wall in…

A: Given Data: Find:

Q: Q.1 Develop an analytical reasoning to prove that the mechanism as shown in Figure.1 have mobility.…

A: To determine:To calculate the mobility

Q: Consider a mass m attached to a spring with natural length 7, hanging vertically under the action of…

A: the motion will be started from that instant when the system is released. ie. at t=0 But analysis of…

Q: 35. A horizontal spring attached to a wall has a force constant QIC of k = 850 N/m. A block of mass…

Q: Answer D

Q: 2- Two mass-spring syst the mass of system B answer with a plot

Q: Figure Q3(b) shows a uniform bar AB of mass = 8 kg hinged at point C. Point A is connected to a…

A: Given data: The mass of the uniform bar AB is (m) =8 kg The stiffness of the spring is (K) = 500 N/m…

Q: Q4. A two-degree-of-freedom model consisting of two masses connected in series by two springs is…

Q: meun y a damper with damping coefficient e, as well as a spring wi /m. Moment of inertia of the…

A: To given thatmass (m1)=1kgmassm2=0.5kgλ=30°spring constant,K=2N/minertia of pulleyJ=0.01Kg.m2Radius…

Q: 1. Consider a damped spring-mass system with m = 1kg, k = 4 kg/s^2 and b = 5 kg/s. a. Write the…

Q: Consider the system shown in Fig.2. The bars have equal lengths LAB = lBC = 1.5 m. Their respective…

Concept explainers

Free Body Diagram

The system of forces acting on a body tends to either rotate it or make the body undergo motion. In general, when an external agent exerts a force on a body, the body undergoes translational motion and rotational motion. The body has six degrees of freedom under the influence of that force. Here, three degrees of freedom are from the translational motion while the other three are from the rotation motion. However, sometimes the bodies are not allowed to undergo any motion and are fixed, under such conditions the body is said to be constrained.

Question

(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
0 = 3.5 degree and released,
(i)
With the free body diagram and kinetic diagram, determine the initial
horizontal displacement of A.
(ii)
Determine the period of vibration.
(iii) Determine the maximum velocity and acceleration at point A.
mive
950 mm
G
40 mm
В
Figure Q3(b)

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

VIEW

Step 2

VIEW

Trending now

This is a popular solution!

Step by step

Solved in 2 steps with 1 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

Q4. A two-degree-of-freedom model consisting of two masses connected in series by two springs is shown in the figure below. The physical parameters have the values m, = 8 kg, m, = 2 kg, k, = 20 N/m, and k2 = 30 N/m. X1 X2 m1 m2 k1 k2 (A) Write down the equation of motion for mass m, (B) Write down the equation of motion for mass m, Calculate the first (larger) natural frequency of the system (D) Calculate the second (smaller) natural frequency of the system
4.13. Derive the differential equation of motion of the system shown in Fig. P4.1. Obtain the steady state solution of the absolute motion of the mass. Also obtain the displacement of the mass with respect to the moving base. For this system, let m=3 kg, k1 =k2 = 1350 N/m, c= 40 N s/m, and y=0.04 sin 15t. The initial conditions are such that xo =5 mm and io =0. Determine the displacement, velocity, and acceleration of the mass after time t =1s. y = Y, sin @,1 k1 in k2 m Fig. P4.1
A wooden plank of mass M is placed on the top of two identical, homogeneous cylinders, each of mass m. The plank is attached to a verti-cal wall with a horizontal ideal spring of stiffness k (see figure). Find the period of small oscillations of the plank. Assume that the coefficient of static friction is large enough so the cylinders don’t slip neither on the horizontal surface nor on the plank.
ANSWER ALL QUESTIONS OTHERWISE DONT ATTEMPT IT STRICTLY.
For each of the systems shown in Figure P4.52, the input is the force f andthe outputs are the displacements x1 and x2 of the masses. The equilibriumpositions with f = 0 correspond to x1 = x2 = 0. Neglect any friction betweenthe masses and the surface. Derive the equations of motion of the systems.
Consider an electrical motor with mass M= 29 kg located at the tip of a rigid beam pivoted at point A, with the other end supported by a spring and damper with stiffness, k = 6 MN/m and damper c= 12 kNs/m, as shown in the figure below. Assume that the rigid beam is massless, the length is L= 1.3 m (horizontal distance between point O and pivot point A), and zero initial conditions. If there is an unbalanced mass of m0=2 kg in the rotating part of the motor, eccentricity is e =382 mm, and the rotor is rotating with a speed of w (omega) = 203 rad/s, determine the maximum amplitude response of point O at steady state condition in millimetre. Assume the line of actions of forces created by spring and damper act through point O, the centre of electric motor. Treat the electric motor mass as a point mass for calculating its moment of inertia about point A.
A simplified SDOF model of a vehicle suspension system is shown in below Figure. The mass of the vehicle is 500 kg. The suspension spring has a stiffness of 100,000 N/m. The wheel is modeled as a spring placed in series with the suspension spring. When the vehicle is empty, its static deflection is measured as 5 cm. (a) Determine the equivalent stiffness of the wheel (b) Determine the equivalent stiffness of the spring combination. (c) Determine the natural frequency fn of the system ks kw m ww Suspension spring Wheel I stiffness
Please find the question attached.
More than one answer is possible
As shown in the figure below, a uniform bar with mass m moves freely along a vertical tube at one end, suspended from a spring, and moving along a horizontal tube. At this time, find the equilibrium state, and find the stability of each. (When the spring constant is k and x=0, the spring is not deformed.)
A beam is supported by a hinged joint at one end (O) and by a spring at the other end (A) as shown in the figure. The stiffness of the spring is such that the beam end A lies directly under the spring attachment point B when the spring is at its free length (no force). Using Hamilton's principle, develop the Euler-Lagrange equation of motion for the system when subjected to 1. A time-dependent vertical force applied at end A of the beam. 2. A time dependent force at end A of the beam that remains oriented perpendicular to the beam for all angles of the beam. Assume the following for your analysis 1. The beam is rigid. 2. The beam is uniform, i.e. its mass per unit length is constant) 3. The thickness of the beam is small compared to its length 4. The spring stiffness is constant. 5. The spring mass is small and can be ignored. 6. The angular displacements of the beam are not necessarily small. D F(t) F(t)
PART OF MECHANICAL VIBRATIONS SUBJECT USE VIRTUAL WORK The uniform bar shown in Fig. P3.6 has mass m, length l, and mass moment of inertia 1 about its mass center. The bar is supported by two springs kı and k2, as shown in the figure. Obtain the differential equation of motion and determine the natural frequency of the system in the case of small oscillations.