A spring-mass-damper system oscillating about the horizontal surface is subjected to an external force of F = 300 sin (6

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A spring-mass-damper system oscillating about the horizontal
surface is subjected to an
external force of F = 300 sin (6)(t), where 300 is in Newtons and 6
is in radians per second. The
system has a mass 90 [kg], a damping coefficient of 78 [N ⋅ s/m]
and a spring constant of
300 [N⁄m]. The system is both given an initial displacement of 1.2
[m] and an initial velocity of 1.4
[m⁄s].
a. Using Method of Undetermined Coefficients, determine the
particular solution for the
displacement function.
b. Determine the unknown coefficients for the homogeneous solution
using the initial
conditions (Note: the external force already works at t =
0).
c. Determine the position, velocity, and acceleration of the system
after 10 seconds.