Q2) Consider a mass (m=5 kg) connected to a masslessrod of length (L=2 m) to swing about point 0, as shownin Figure (2). The mauss is also connected to a spring ofspring constant (k=10 N/m). The other end of thespring is connected to a pivot. The unstreteched lengthof the spring is I m. Find the equation of motion of thesystem.NinFigure 2

Answered: Image /qna-images/answer/d000e7f4-e755-432a-bb8e-af4d020c97d6.jpg

a mass (m-5 kg) connected to a massless rod of length (L=2 m) to swing about point 0. as shown in Figure (2). The mauss is also connected to a spring of spring constant (k=10 Nim). The other end of the spring is conected to a pivot. The unstretched length of the spring is I m. Find the equation of motion of the system.

a mass (m-5 kg) connected to a massless rod of length (L=2 m) to swing about point 0. as shown in Figure (2). The mauss is also connected to a spring of spring constant (k=10 Nim). The other end of the spring is conected to a pivot. The unstretched length of the spring is I m. Find the equation of motion of the system.

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: Problem 2: Suppose the massless rod in the discussion of the nonlinear pendulum is a string of…

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: Example(1):- A rope (AB) of length 35 m passing over a pulley of negligible size at (C) as shown in…

Q: A uniform plank of length 2.00 m and mass 35.0 kg is supported by three ropes, as indicated by the…

Q: 4. Consider the following spring-mass systems below with zero initial conditions described as x (0)…

A: Please find the below attached solution of problem given,feel free to ask any further…

Q: A mass, m, is supported on a light beam, which is free to rotate about the pivot at O as illustrated…

Q: For the system shown in Figure Q 4: (i) Draw the free body diagram (i1) Formulate the equation of…

A: Consider a system having mass M attached by two spring and fixed at another end on the wall.…

Q: Using the figure below for a mass-spring system and given that R2 = 2R1, derive the equation of…

Q: A two-link mechanism (AB and BC) makes contact with a disk of radius R = 0.1 m at point C (a…

Q: 1. Consider the system shown in the Figure P1, where ky is torsional stiffness. Assume that the…

Q: A wheel is fixed at its center position and allowed to rotate. The moment of inertia of the wheel is…

A: Given: To find: Equation of motion

Q: Figure 1.1 shows a crank, OA = 72 mm long which rotates anticlockwise about 0 at w = 150 rev min A…

A: Refer the answer in the next page.

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

Q: Derive the differential equation of motion for the system shoen in Figure () in terms of the…

Q: Find the equilibrium positions of this system and linearize the system about two of its equilibrium…

A: DefinitionOne Degree of Freedom System:A system that can only move in one direction or rotate about…

Q: Q4) Derive the equation of motion of figure 4.

A: Given Data: The mass of the slender rod is m. The spring constant of the springs is k. The damping…

Q: The system is now modified, with different values of spring stiffness and damping coefficient…

A: Given:To find:Steady state amplitudePeak amplitude

Concept explainers

Free undamped vibrations

Whenever an object/system displaces in either side of its equilibrium position with the help of an external/internal means, then the object/system moves regularly or randomly on both sides of its equilibrium position. This motion is called vibration. Generally, there are three types of vibration: longitudinal vibration, transverse vibration, and torsional vibration.

Question

Q2) Consider a mass (m=5 kg) connected to a massless
rod of length (L=2 m) to swing about point 0, as shown
in Figure (2). The mauss is also connected to a spring of
spring constant (k=10 N/m). The other end of the
spring is connected to a pivot. The unstreteched length
of the spring is I m. Find the equation of motion of the
system.
Nin
Figure 2

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 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

The single degree of freedom system shown in Figure 3 is at its undeformed position. The SDOF system consists of a rigid beam that is massless. The rigid beam has a pinned (i.e., zero moment) connection to the wall (left end) and it supports a mass m on its right end. The rigid beam is supported by two springs. Both springs have the same stiffness k. The first spring is located at distance L/4 from the left support, where L is the length of the rigid beam. The second spring is located at distance L from the left support. Rigid, Massless Beam with pin end k m u(t) Figure 3: Single-degree-of-freedom system in Problem 3. Please compute the following: (a) Find the expression of the effective stiffness of the SDOF system (b) Derive the equation of motion of the mass m. (c) Find the expression of the expression of its natural period.
B3
system with m=20, c = 17 Suppose that the mass in a mass-spring-dashpot and k = 3 is set in motion with x(0) = 0 and x'(0) = 8. (a) Find the position function x(t) and show that its graph looks as indicated in the figure. (b) Find how far the mass moves to the right before starting back toward the origin. 3 5 160 (a) x(t) = 7 (Type an exact answer.) 160 7 300 (b) The mass moves 7.1344 units to the right before turning back. (Round to four decimal places as needed.) 0 10 20 30 40 50
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
A spring connects mass m of a pendulum to a wall as shown in the figure. The original un- stretched length of the spring is L. Use the Energy Method and find the equation of motion of the system in terms of the angle 0. L L K m Original Length = L
A pendulum is made up of a spring with a mass attached to the end. The spring is arranged to lie in a straight line, by wrapping the spring around a massless bar. The equilibrium length of the bar is “l”. Using lagrange’s equations, find the equations of motion.
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)
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.
A body weighing 5kg is attached to a very light bar as depicted below. The set-up is free to rotate in the vertical plane about pin support O. The force applied at point C makes the bar oscillate(via small rotation) about the position of equilibrium illustrated below a. Derive the differential equation of motion for the steady state angular displacement (theta) of the bar
An undamped spring/mass system, in which m = 8 slugs and the spring constant k = 16 lb/ft has a driving force f(t) = t^pi*t on [0,pi] Extend f(t) into the negative t-axis to obtain an odd function. Find the particular solution ??(?). (Note: f(t) is given as half of the period, p = π.)
0.5m 1m The figure shows a slender rod with a mass of 6 kg. Attached to the rod is a spring of stiffness k = 250 N /m .A moveable point mass m1= 1 kg is position at a distance x from the pivot point. You can assume small angle oscillations from the equilibrium position shown in the figure.
Problem (1): Derive the equation of motion of the system shown in Figure and find: • The natural frequency of vibration • The damping ratio • The free damped frequency of vibration If m= 10 kg, c = 50 N-s/m, k = 1000 N/m, L= 1 m 44 3k Uniform rigid bar, mass m 2 2