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There is a spring-mass system, driven by an external piston, which applies a force to it. Newtons that satisfies the following relation F = 6*cos (3*π*t), as can be seen in the figure, it is known that the spring constant has a value of k = 25 Nm, and the block has a mass of 4 kg, furthermore, dissipative frictional effects cause the relationship between velocity and force to satisfy the ratio F = bv, where b is the damping constant, and it is known that the numerical ratio of force is 10 times the value of speed.
Determine:
a) The natural frequency of the system.
b) The driving frequency of the external force.
c) The maximum value exerted by the external force.
d) The damping constant.
e) The amplitude of the forced oscillatory motion in steady state.
f) If dissipative (damping) effects are neglected, what is the value of the amplitude.
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