Question

Starting from first principles, determine the equation of motion for the system shown.

1. Draw free body diagram for small displacements measured from static equilibrium.
2. Take moments about the hinge to obtain the equation of motion as.

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Answer 1

Given that E Sin wt k 1 ***** At mean position Estatic equillubrium) (4-0) Yus mg & = k xl@; Х If Х alt 4 mg 1/2 = k0i (24) 2 Now, at t=t to +0o) a Fobin tok mg 7 unt

=0 using first principle -P3 + (+ 6 () + 6 +16 (Sina) 4 -mg + Koi (24) t ko ( 3 ) 2 + ce²6 +18 + (Fo Sin wd) - now from equation (is that mge = kai ( 34 ) 2 K8 (*) 7 cepe tcd²e + 1 8 + (Fo Sin wat) 1 - 2 Io + 9 ke²a+ ce²8 -(Fo sin wat ek motion. I= -> this is the basic equation of to from hing. I mer me ö + + fake's + -keho + cd²i = -(to sin wat e ät 2 ke2 e ce? - (Fo Sin wt) mer 3 -3 fo Sin wt — 2 = + 2) me? 2 mi 3 - 2 e o+27k 16 m

comment ; In above solution, = rate of change of angle lie, angular 0. velocity ө 6 = angular acceleration angular distalacement solving the above equation , we and on will get the the solution of equation.