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4. Point mass m is attochad to o Axed seying mechanism of the form Y such tha+ ue have orltcal damplng so the functian of the. moal from tRe equilloriu (02lfthe sastem s tos its mohemeni at Hime to with intiol devioton xo and inltol elocity Vo, b) f Uo woxo show hat e sqstem posses equilibriom posltion Only ohce, colculon he Cornesponding tine to and t system will perform a uoou damplng osallotion and calasloette fequoncy of thls oscMMation and he & quality foctor 4. Point mass m is attached to a fixed spring with a constant spring s and a friction mechanism of the form F--r * v, r such that we have critical damping, so the function of the removal from the equilibrium state is of the form x(t) (A+ Bt )exp(-yt), (y-r/ 2nm (a)If the system starts its movement at time t- 0, with initial deviation x0 and initial velocity v0, calculate the constants A and B. (b) IfvO- 2ω0 * x0 , show that the system passes the equilibrium position only once, calculate the corresponding time t-0, and the corresponding transit speed. (c) If we change the coefficient of friction to a new value r -[(sm) A 1/2 ]/ 2, show that the system will perform a weak damping oscillation and calculate the frequency of this oscillation and the Q quality factor.

Answer 1

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