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Tutorial $5$

Done

$3$ of $5$ tural trequency of the system.

m uasinur ui uriniown damping coefficient is added to the system. In order to find out the damping in the system the mass is subjected to a harmonic force $F=(100sin12t)N,$ time is in seconds. The recorded steady$-$state amplitude is $0\mathrm{.}01$ m $.$

b$)$ Determine the damping coefficient of the dashpot.

Ans: a$)12ra\frac{d}{s}$; b$)0\mathrm{.}347$

Question $5$

The equation of motion of a spring$-$damper mass system under the action of a harmonic force $F(t)=0\mathrm{.}4sin3t$ is given by:

$2x^{}+8x^{}+128x=F(t)$

Spring$-$mass$-$damper system under the action of a harmonic force

Where the time is given in seconds and the value of the force in N $.$

a$)$ Determine the damping ratio of the system

b$)$ Calculate the steady$-$state amplitude of the system

c$)$ Calculate the phase of the steadystate amplitude of the block.

d$)$ What is the estimated value of the frequency $($in Hz $)$ where you expect the maximum amplitude of the response to harmonic excitation

e$)$ If the motion of the block starts from rest, write the displacement of the block as a function of time $x(t).$

Ans: a$)0\mathrm{.}25$ ; b$)x(3)=$

$\frac{0\mathrm{.}1}{\sqrt[\phantom{2}]{(-9+64{)}^2+(4**3{)}^2}}=3\mathrm{.}55mm$;

c$)(3)=$atan$(\frac{4**3}{9-64})=-0\mathrm{.}215$rad$=-$

$12\mathrm{.}3$ deg;

d$)1\mathrm{.}191$ Hz ;

e$)$ in mm See the graphical representation of the frequency response of the system.

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