A spring is such that a force of 20 [N] would stretch it 0.2[m]. The spring hangs vertically and a 4 [kg] mass is attached to the end of it. After this mass comes to rest in its equilibrium position, it is pulled down [0.4 [m] below this position and then released at t = 0. The medium offers a resistance 2dx/dt, where dx/dt is the instantaneous velocity in [m/s] (a) Determine the displacement of the weight as a function of the time and express this displacement in the amplitude-phase form (b) Find the so-called "period" and determine the logarithmic decrements. (c) At what time does the weight first pass through its equilibrium position?

A spring is such that a force of 20 [N] would stretch it 0.2[m]. The spring hangs vertically and a 4 [kg] mass is attached to the end of it. After this mass comes to rest in its equilibrium position, it is pulled down [0.4 [m] below this position and then released at t = 0. The medium offers a resistance 2dx/dt, where dx/dt is the instantaneous velocity in [m/s] (a) Determine the displacement of the weight as a function of the time and express this displacement in the amplitude-phase form (b) Find the so-called "period" and determine the logarithmic decrements. (c) At what time does the weight first pass through its equilibrium position?

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Question

(a) Determine the displacement of the weight as a function of the time and express this displacement in the amplitude-phase form

(b) Find the so-called "period" and determine the logarithmic decrements.

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