Consider the perfectly rigid uniform bar shown in Figure 1. The springs are unstretched when the bar is horizontal.
Physical constants for the system are given in the picture caption.
$k_1$
$L_1$
$L_2$
$L$
$c$
$k_2$
Figure 1: $9.45kg$ uniform rigid bar subject to rotational vibration with $L_1 = 0.34m$, $L_2 = 0.663m$, $L = 0.896m$, $k_1 = 458N/m$, $k_2 = 647N/m$, and $c = 10.2187N \cdot s/m$.
(a) Determine the undamped natural frequency of the system, the damping ratio, the logarithmic decrement and the frequency of damped vibration.
(b) When the bar is released from rest with an initial counterclockwise rotation of $\theta = 0.062radians$ about the bearing, determine the resulting expression for the angle of the bar as a function of time.
