The system shown consists of a mass m and a massless rod of length l. The system is supported by two springs which have stiffness coefficients k1 and k2, as shown in the figure. Derive the system differential equation of motion assuming small oscillations. Determine the natural frequency of the system.

The system shown consists of a mass m and a massless rod of length l. The system is supported by two springs which have stiffness coefficients k1 and k2, as shown in the figure. Derive the system differential equation of motion assuming small oscillations. Determine the natural frequency 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: Write the equation of motion of the system using D'Alemberts principle. Find the natural frequency…

Q: Derive the expression for motion and determine the natural frequency of the system shown in the…

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 homogeneous rod OA is supported at point 0, and a mass of 2m is attached at the bottom of the…

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

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: 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: A mass m is attached to both a spring (with given spring constant k) and a dashpot (with given…

A: Solution: Given Data: m=25 kgc=50 N-s/mk=169 N/mxo=5 mvo=16 m/s To Find: xt=C1e-ptcosω1t-α1u(t) =…

Q: A uniform rigid bar of length L and mass m is pinned at one end and restrained by a spring as shown…

Q: 35 N.s/m 150 N/m 750 mm 750 mm- 150 N/m 1000 mm 20 sin 5t N с 15 kg www.

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: You have a prototype Slinky with a lump of coal at the end. This forms a damped spring-mass system.…

A: Here Given:- m=1 k=3 b=1

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

Question

100%

The system shown consists of a mass m and a massless rod of
length l. The system is supported by two springs which have stiffness coefficients k1 and k2, as shown in the figure. Derive the system differential equation
of motion assuming small oscillations. Determine the natural frequency of the
system.

The system shown consists of a mass m and a massless rod of
length 1. The system is supported by two springs which have stiffness coeffi-
cients kj and k2, as shown in the figure. Derive the system differential equation
of motion assuming small oscillations. Determine the natural frequency of the
system.

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

Step 3

VIEW

Trending now

This is a popular solution!

Step by step

Solved in 3 steps with 3 images

SEE SOLUTION Check out a sample Q&A here

Similar questions

A mass m is attached to both a spring (with given spring constant k) and a dashpot (with given damping constant c). The mass is set in motion with initial position x0 and initial velocity v0. Find the position function x(t) and determine whether the motion is over-damped, critically damped, or under-damped.
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)
Q4/ The flywheel of an engine driving a dynamo has a mass of 180 kg and a radius of gyration of 30 mm. The shaft at the flywheel end has an effective length of 250 mm and is 50 mm diameter. The armature mass is 120 kg and its radius of gyration is 22.5 mm. The dynamo shaft is 34 mm diameter and 200 mm effective length. Calculate the position of node and frequency of torsional oscillation. G = 83 kN/mm².
14. For the system shown to the right, the disk of mass m rolls without slip and z measures the displaccment of the disk from the unstretchcd position of the spring. 3k a) find the cquations of motion; b) if the system is inderdamped, whiat is the frequency of the frec vibrations of this system in terms of the parancters k, с, and m;
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
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.
Question 2 A pendulum consisting of a bar “B” and a mass “C” is suspended from a fixed pivot at “O” as shown in figure 2– a. A light spring is attached to the pendulum at point “P” and is anchored at a fixed point “Q”. When the pendulum is in equilibrium the line OC is at 450 from the vertical and the angle OPQ is 900. Calculate the natural frequency of the pendulum for small oscillations about the equilibrium position. The following data is available: Bar “B” Mass “C” Spring PQ mass 1 kg 6 kg centre of gravity G1 G2 radius of gyration about the centre of gravity 0,1 m 0,025 m spring stiffness 700 N/m
An sdof system consists of mass 175 kg and a spring constant k 530 kn/m while testing the system a relative velocity of 0.3 m was observed on application of force of 450 n determine the damping ratio
6. Derive the equation of motion for x2 as function of Fa. The indicated damping is viscous. Fa k m₁ mmmm M₂ rooooo
4. A mass-spring system exhibits a period of 5 s and a measured mass of 20 kg. Calculate the spring stiffness k.
Consider the mechanical system of this figure comprising two wheels of mass m, inertia j, andthree springs each of stiffness k. The wheels move on two fixed horizontal surfaces during thesystem's free vibrations. Derive the mathematical model of this mechanical system.