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A 10.6-kg object oscillates at the end of a horizontal spring that has a spring constant of 2.05 x 104 N.m. The effect of friction force is represented by the damping coefficient b= 3.00 N.s.m!. C. 1) Set up the differential equation of motion for oscillations of the system. C. 2) Show that x(t) = Aoe- equation found in part C. a). C. 3) Draw a representative figure for the damped vibration x(t). C. 4) Calculate the angular frequency wo (o 00) and the period T. -bt/2m cos(wt + @) is a solution for the previous %3D Calculate the frequency of the damped oscillation.

A 10.6-kg object oscillates at the end of a horizontal spring that has a spring constant of 2.05 x 104 N.m. The effect of friction force is represented by the damping coefficient b= 3.00 N.s.m!. C. 1) Set up the differential equation of motion for oscillations of the system. C. 2) Show that x(t) = Aoe- equation found in part C. a). C. 3) Draw a representative figure for the damped vibration x(t). C. 4) Calculate the angular frequency wo (o 00) and the period T. -bt/2m cos(wt + @) is a solution for the previous %3D Calculate the frequency of the damped oscillation.

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C. Numerical applications: A 10.6-kg object oscillates at the end of a horizontal spring that has a spring constant of 2.05 x 104 N.ml. The effect of friction force is represented by the damping coefficient b= 3.00 N.s.ml. C. 1) Set up the differential equation of motion for oscillations of the system. C. 2) Show that x(t) = Ane-bt/2m equation found in part C. a). C. 3) Draw a representative figure for the damped vibration x(t). C. 4) Calculate the angular freqiency oo ( 00) and the period T. cos(@t + o) is a solution for the previous Calculate the frequency of the damped oscillation. 梦 $ (3) a.
Transcribed Image Text:C. Numerical applications: A 10.6-kg object oscillates at the end of a horizontal spring that has a spring constant of 2.05 x 104 N.ml. The effect of friction force is represented by the damping coefficient b= 3.00 N.s.ml. C. 1) Set up the differential equation of motion for oscillations of the system. C. 2) Show that x(t) = Ane-bt/2m equation found in part C. a). C. 3) Draw a representative figure for the damped vibration x(t). C. 4) Calculate the angular freqiency oo ( 00) and the period T. cos(@t + o) is a solution for the previous Calculate the frequency of the damped oscillation. 梦 $ (3) a.
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