Q2. Derive the equation of motion and find the natural frequency of vibration of the system shown in Figure (a) below. ww Fic. (a)

(1) A rigid bar (OA)with mass m and length L is simply supported at one end and free at the other end .A lumped mass M fixed at the end of A is subjected to a vertical harmonic excitation f(t). Two springs(k) are connected at the length a and b of the bar. Please calculate the natural frequency w and response vibration of the system. (Figure 1) Note: m=10kg, L=1 m, a=0.25m, b=0.5m, k=5000N/m, M=50kg, f(t)=Fcos2t (F=500N, Q=1000rpm). The vibration is very small. a b k L MA m M Figure 1: Single Degree Vibration System f(t) A X

PROBLEM1: Determine the equation of motion of the following systems: 1080 al*k www 0.51 ghiv Vin & Mass Less, Rigid L J Figure 2-Problem 1-2 a3*m

Pls see question in the attached image and solve the question by hand written notes and figure.