SOLUTION:1Magnitude-generally refers to the maximum value ofa signal2.Range-differenceberweenmaximumandminimumvaluesofasignal3.Amplitude-indicative of signal fluctuations relativeto the mean4.Frequency-describesthetimevariationofasignal5.Dynamic-signal istime varying6. Static -signal does not change over the time period of interest7.Deterministic -signal can be described by an equation(other than a Fourier series or integral approximation)8.Non-deterministic-describes a signal which has no discernible pattern of repetitionandcannot be described bya simple equation.9. Determine the average and rms values for the functiony(t) = 25 + 10sin 6t over the time periods(a) 0 to 0.1 s,(b) 0.4 to 0.5 s,(c) 0 to 1/3 s,and(d) 0 to 20 s.Comment on the nature and meaning of the results interms of analysis of dynamic signals.(5p)SOLUTION:For the function y()dand-[oaYrmThus in general.(30+2cos6元l)d=12-5ael1-4[0(5-)+(in6m-sin6m)6.2-4,LandX(30+2cos6m）dt90i+inc12元6元
9. Determine the average and rms values for the functiony(t) = 25 + 10 sin 6t over the time periods(a) 0 to 0.1 s,(b) 0.4 to 0.5 s,(c) 0 to 1/3 s, and(d) 0 to 20 s.Comment on the nature and meaning of the results in terms of analysis of dynamic signals.(5p)
The resultingvalues areJm=31.02a)J=31.01b)J=28.99Jmm=29.00c)y=30Jm=30.03d) j=30mm=30.0310. Determine the value of the spring constant that would result in aspring-mass system thatwould execute one complete cycle of oscillation every 2.7 s, for a massof o.5 kg.Whatnatural frequency does this system exhibit inradians/second?(5p)SOLUTION:Since区0-Vm(asshowninassociationwithequation2.7)andT-2元_1=2.7sof0=2.33rad/sThenaturalfrequency isthenfound as=2.33rad/sAndk0=2.33=V0.5kgk=2.71N/m(kg/sec)11.A spring withk=5000N/cm supports a mass of 1kg.Determine thenatural frequency of this system in radians/second and hertz. (5p)
10. Determine the value of the spring constant that would result in a spring-mass system that would execute one complete cycle of oscillation every 2.7 s, for a mass of 0.5 kg. Whatnatural frequency does this system exhibit in radians/second?(5p) 11. A spring with k = 5000 N/cm supports a mass of 1 kg. Determine the natural frequency of this system in radians/second and hertz. (5p)