Answer:
The answer is
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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
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,
