Answer:
The answer is
"
".
Explanation:
Taking into consideration a volume weight = 16 pounds originally extends a springs
feet but is extracted to resting at 2 feet beneath balance position.
The mass value is =

The source of the hooks law is stable,

Number
times the immediate speed, i.e .. Damping force

The m^2+m+12=0 and m is an auxiliary equation,

Therefore, additional feature
![x_c (t) = e^{\frac{-t}{2}}[C_1 \cos \frac{\sqrt{47}}{2}t+ C_2 \sin \frac{\sqrt{47}}{2}t]](https://tex.z-dn.net/?f=x_c%20%28t%29%20%3D%20e%5E%7B%5Cfrac%7B-t%7D%7B2%7D%7D%5BC_1%20%5Ccos%20%5Cfrac%7B%5Csqrt%7B47%7D%7D%7B2%7Dt%2B%20C_2%20%5Csin%20%5Cfrac%7B%5Csqrt%7B47%7D%7D%7B2%7Dt%5D)
Use the form of uncertain coefficients to find a particular solution.
Assume that solution equation,

These values are replaced by equation ( 1):

Going to compare cos3 t and sin 3 t coefficients from both sides,
The cost3 t is 3A + 3B= 20 coefficients
The sin 3 t is 3B -3A = 0 coefficient
The two equations solved:

Replace the very first equation with the meaning,

equation is

The ultimate plan for both the equation is therefore

Initially, the volume of rest x(0)=2 and x'(0) is extracted by rest i.e.
Throughout the general solution, replace initial state x(0) = 2,
Replace x'(0)=0 with a general solution in the initial condition,
![x(t)= e^\frac{-t}{2} [(c_1 cos \frac{\sqrt{47}}{2}t)+c_2\sin\frac{\sqrt{47}}{2}t)+\frac{10}{3}\cos (3t)+\frac{10}{3}\sin (3t)]\\\\](https://tex.z-dn.net/?f=x%28t%29%3D%20e%5E%5Cfrac%7B-t%7D%7B2%7D%20%5B%28c_1%20cos%20%5Cfrac%7B%5Csqrt%7B47%7D%7D%7B2%7Dt%29%2Bc_2%5Csin%5Cfrac%7B%5Csqrt%7B47%7D%7D%7B2%7Dt%29%2B%5Cfrac%7B10%7D%7B3%7D%5Ccos%20%283t%29%2B%5Cfrac%7B10%7D%7B3%7D%5Csin%20%283t%29%5D%5C%5C%5C%5C)


