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Matlab plots

  1. Apr 13, 2013 #1
    1. The problem statement, all variables and given/known data

    Oscillation in mechanical structures can often be described by the function:

    y(t)=(e^(-t/τ))*sin(ωt+θ)

    Where t is time , ω is oscillation frequency in radians per unit time. The oscillations have a period of 2*π/ω and their amplitudes decay in time at a rate determined by τ which is called the time constant. THe smaller the value of τ the faster the oscillations die out/


    2. Relevant equations

    a.) Use the above information to develop a criterion for choosing the spacing of t values and the upper limit on t to obtain an accurate plot of y(t). (Hint two cases: 4τ>2π/ω and 4τ<2π/ω)

    b) Plot y(t) for τ= 10, ω=π and θ=2

    c)Plot y(t) for τ= 0.1, ω=8π and θ=2


    3. The attempt at a solution

    My attempt is below, however what is bothering me is question (a). A criterion for choosing the spacing values for t and the upper limit. ?? Can't figure it out and also the hint.. How is that related? I just played around with numbers, and got those plots.



    tau=10;
    omega=pi;
    fi=2;
    t=(-40:0.1:10);
    f=(exp(-t./tau)).*sin(omega.*t+fi);
    subplot(2,1,1)
    plot(t,f)

    tau2=0.1;
    omega2=8*pi;
    fi=2;
    t=(-0:0.1:80);
    f2=(exp(-t./tau2)).*sin(omega2.*t+fi);
    subplot(2,1,2)
    plot(t,f2)
     
  2. jcsd
  3. Apr 14, 2013 #2

    Simon Bridge

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    Try playing around some more then and see what makes the spacing of t values too big.
    What do the two limiting cases represent physically?
     
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