A uniform bar of mass m is pivoted at point O and supported at the ends by two springs, and damper at middle, as shown. End P of spring PQ is subjected to a sinusoidal force F= Fo cos wot. If it given that; 1=zm, k=ykN/m, c= 100 N.s/m, m = 3(x) kg, wo = 20 rad/s and Fo= 100(x) N. (if z = 0, use l = 1 m) i. Drive the differential equation that describes the motion of the bar. ii. Calculate the natural frequency of the bar. iii. Calculate the damping frequency of the bar. iv. Find the steady-state angular displacement of the bar. v. Calculate the magnification factor (MF). Free 44 I 1-4-1 - X=8, Y=8, Z=2 Fo cos at Uniform bar, mass m -1/12 P 0xxxx Q k