Analytical Mech Homework Solutions 23

Analytical Mech Homework Solutions 23 - 3.6 3.7 1 1 l = T =...

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3.6 11 2.5 9.8 2 6 l Ts g ππ == D s 3.7 For springs tied in parallel: () ( ) 12 1 2 s Fx k xkx k kx =− + () 1 2 kk m ω +  =   For springs tied in series: The upward force is m eq k x . Therefore, the downward force on spring is 2 k eq k x . The upward force on the spring is 2 k 1 kx where x is the displacement of P, the point at which the springs are tied. Since the spring is in equilibrium, 2 k 1 eq k ′ = x . Meanwhile, The upward force at P is 1 . The downward force at P is ( ) 2 kxx . Therefore, k x x ′′
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