taller 1 vibraciones libres

8/17/2019 TALLER 1 Vibraciones Libres

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TALLER 1: Vibraciones Libres

Ecuaciones1. Resolver en Mathcad las siguientes ecuaciones características y evalúelas

gráca!ente:

E"e!#lo resuelto



$roble!as

1. A single degree of freedom mass-spring system consistsof a 10 kgs mass suspendedby a linear spring which has a stiffness coefficient of 6 x 103N/m !he mass is gi"en an initial displacement of 00# mand it is released from rest$etermine the differential e%uation of motion& and the

natural fre%uency of the system $etermine also themaximum "elocity

'olution(



) !he oscillatory motion of an undamped single degree offreedom system is such that the mass has maximumacceleration of *0 m/s) and has natural fre%uencyof 30 +, $etermine the amplitude of "ibration and themaximum "elocity



3 A single degree of freedom undamped mass-springsystem is subected to an impact loading which results in aninitial "elocity of * m/s. .f the mass is e%ual to 10 kg and thespring stiffness is e%ual to 6 x 103 N/m, determine the

system response as a function of time

'olution(

# !he undamped single degree offreedom system ofroblem 1 is subected to the initial conditions Xo 00) mand o 3 m/s. $etermine the system response as afunction of time Also determine the maximum "elocity andthe total energy of the system

1 rad%s & 1%'( )* & +.1,-1,- )*



* !he system shown in 2ig # consists of a uniform rodwhich has length I, mass m, and mass moment of inertiaabout its mass center I. !he rod is supported bytwo springs which ha"e stiffness coefficients kl and k2' as

shown in the figure $etermine the system differentiale%uation of motion for small oscillations $etermine also thesystem natural fre%uency

/olution0ree body diagra!



6 !he system shown in 2ig 6 consists of a mass m and auniform circular rod of mass m" length I, and mass momentof inertia I about its mass center !he rod is connected to

the ground by a spring which has a stiffness coefficient k. Assuming small oscillations& deri"e the system differentiale%uation of motion and determine the natural fre%uency ofthe system $etermine the system response as a function of time



.f the shafts shown in 2ig ha"e modulus of rigidity 41and 4) & deri"e the differential e%uation of the system anddetermine the system natural fre%uency

solution

2ree body diagram



!he uniform bar shown in 2ig l0 has mass m,

length /& and mass moment of inertia I about its masscenter !he bar is supported by two springs kl and

k2, as shown in the figure 7btain the differentiale%uation of motion and determinethe natural fre%uency of the system for smalloscillation.

2ig 10solution2ree body diagram



10!he system shown in 2ig 1) consists of a uniform barand a mass m, rigidly attached to one end of the bar !hebar is connected to the ground by a pin oint at 7 !he

system is supported by two springs which ha"e stiffnesscoefficients k, and k2 . !he bar has length .& mass m, andmass moment of inertia I. $eri"e the system e%uation ofmotion and determine the natural fre%uency

2ig 1)

.mpares resueltos

31 1

3) )33 33# #3&11 *313 631# 31* 531

315 10

taller 1 vibraciones libres

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