Part a The text describes a physics problem related to a damped harmonic oscillator system:---A 1-kg mass is attached to a spring with a stiffness of 1 N/m. The damping constant for the system is 2 N-sec/m. At time \( t = 0 \), the mass is compressed 20 cm (0.2 m) to the left and given an initial velocity of 30 cm/sec (0.3 m/sec) to the right.(a) The position \( x(t) \) of the mass at time \( t \) is given by:- **A.** \( x(t) = \frac{{\sin t - 2 \cos t}}{10} e^{-t} \)- **B.** \( x(t) = \frac{{2 - t}}{10} e^{t} \)- **C.** \( x(t) = \frac{{t - 2}}{10} e^{-t} \)- **D.** \( x(t) = \frac{{4 \sqrt{3} \sin \frac{\sqrt{3} t}{2} - 6 \cos \frac{\sqrt{3} t}{2}}}{30} e^{-\frac{t}{2}} \)- **E.** None of the given answers are correct---No graphs or diagrams are present in the image. The problem involves selecting the correct formula for the position of the mass as a function of time, considering the given conditions of an initial compression and velocity, with a specified damping constant.

Answered: Image /qna-images/answer/79a095a4-14c1-475b-96fa-46a61d440974.jpg

A 1-kg mass is attached to a spring with stiffness 1 N/m. The damping constant for the suystem is 2 N-sec/m. At time t=0, the mass is compressed 20 cm (=0.2 m) to the left and given an initial velocity of 30 cm/sec (=0.3 m/sec) to the right. (a) The position x(t) of the mass at time t is given by OA. sint -2 cos t 10 O B. O C. O D. x(t) = x(t)= x(t) = 2-1 10 t-2 10 et -t 4√3 sin √3t 2 -t e - 6 cos x(t) = 30 OE. None of the given answer √3t 2 ect