Ask a question from expert

Ask now

ENS6160: Signals & Systems

12 Pages720 Words276 Views
   

Edith Cowan University Australia

   

Signals & Systems (ENS6160)

   

Added on  2020-05-04

ENS6160: Signals & Systems

   

Edith Cowan University Australia

   

Signals & Systems (ENS6160)

   Added on 2020-05-04

BookmarkShareRelated Documents
ENS6160: Signals & Systems_1
ASSIGNMENT 1UNIVERSITY AFFILIATION|DATE OF SUBMISSIONASSIGNMENTSTUDENT NAME
ENS6160: Signals & Systems_2
ASSIGNMENT 2ANALYSING A SIMPLE SYSTEMSection 1: Mathematical Analysis of System (20 marks)Note that the voltage output, V, is proportional to the change in the difference between x and y due to piezoelectric effect. (i)Free body diagram(ii)The accelerometer is a damped second order system. It is expressed by the homogenous second order DE for such a damped system asShow that the motion of the accelerometer can be described by the LCCDE below,For forced vibrations the equation of motion is given as follows,newton'ssecondlawofmotionF=maFappliedFdampingFspring=ma=m ̈z(t)m ̈z(t)+Fdamping+Fspring=FappliedApplying the newton’s law to a free-body diagram of the mass,
ENS6160: Signals & Systems_3
ASSIGNMENT 3m ̈x=F=FbFk+Fm ̈z=b ̇zkz+FThe equation is rearranged to standard to form a homogenous second order ODE,m ̈z+b ̇z+kz=FIn standard form, it is expressed as, ̈z+[bm] ̇z+[km]z=[Fm]In the free body diagram, let b=C, and F/m = u[bm]2ζwn[km]wn2 ̈z+2ζwn ̇z+wn2z=uFor a free vibration system, u=0 ̈z+2ζwn ̇z+wn2z=0(iii)The expression for the damping ration and natural frequency in terms of m, k, c¿[km]ωn2,ωn=km...naturalfrequency¿[bm]2ζwn,ζ=b2mwn...dampingratio(iv)Characteristic equation and eigen values for the system ̈z+2ζwn ̇z+wn2z=0...characteristicequationSolution to the characteristic equationz1,z2=c±c24km2mλ=ζωn±ωnζ21(v)Natural response for system (a)0<ζ <1 (b)ζ =1(c)ζ>1Substituting in the equation above,λ=ζωn±ωnζ21For part a,ζ21,ζ<1underdamped
ENS6160: Signals & Systems_4

End of preview

Want to access all the pages? Upload your documents or become a member.

Related Documents
Vibration Analysis and Modeling of Automobile Suspension Systems
|17
|1988
|300