SolSec3_4 - 3- 50Problems and Solutions for Section 3.4...

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Unformatted text preview: 3- 50Problems and Solutions for Section 3.4 (3.35 through 3.38) 3.35Calculate the response of m!!x+c!x+kx=F!(t)where Φ(t) is the unit step function for the case with x= v= 0. Use the Laplace transform method and assume that the system is underdamped. Solution: Given: m!!x+c!x+kx=Fμ(t)!!x+2!"n!x+"n2x=Fmμ(t) (!<1)Take Laplace Transform: s2X(s)+2!"nsX(s)+"n2X(s)=Fm1s#$%&’(X(s)=F/ms2+2!"ns+"n2( )s=Fm"n2#$%&’("n2s s2+2!"ns+"n2( )Using inverse Laplace tables, x(t)=Fk!Fk1!"2e!"#ntsin#n1!"2t+cos!1(")( )3- 513.36Using the Laplace transform method, calculate the response of the system of Example 3.4.4 for the overdamped case (ζ> 1). Plot the response for m= 1 kg, k= 100 N/m, and ζ= 1.5. Solution: From example 3.4.4, m!!x+c!x+kx=!(t)!!x+2"#n!x+#n2x=1m!(t) (">1)Take Laplace Transform: s2X(s)+2!"nsX(s)+"n2X(s)=1mX(s)=1/ms2+2!"ns+"n2=1/m(s+a)(s+b)Using inverse Laplace tables,a=!"#n+#n"2!1, b=!...
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SolSec3_4 - 3- 50Problems and Solutions for Section 3.4...

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