hwk11_soln

hwk11_soln - Problem 11.1 SOLUTION Consider the undamped...

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Unformatted text preview: Problem 11.1 - SOLUTION Consider the undamped single-DOF system shown below, where m = 2 kg and k 1 = 1600 N / m . The applied force, f(t), has an impulse of I = 5 N ⋅ sec . a) Derive the EOM for the system in terms of the generalized coordinate x. The springs are unstretched when x = 0. b) If f ( t ) = I δ ( t ) (where δ ( t ) is the Dirac delta function) and k 2 = k 1 , determine the maximum response x max . c) If f ( t ) is the pulse function shown below and k 2 = k 1 , determine the maximum response x max . Compare with that found in b) above. d) Consider again the pulse excitation f ( t ) shown below but here k 2 ≠ k 1 . Determine the range of values of k 2 for which the system is shock isolated. The two springs are in series and are equivalent to a single spring of stiffness: k = 1 k 1 + 1 k 2 ⎛ ⎝ ⎜ ⎞ ⎠ ⎟ − 1 = k 1 k 2 k 1 + k 2 Therefore, for this problem: T = 1 2 m x 2 U = 1 2 kx 2 dW = f t ( ) dx ⇒ Q = f t ( ) m k 1 x k 2 f t ( ) t f t ( ) I = 5 N ! sec T = 0.05 sec From Lagrange’s equations, the EOM becomes: m x + kx = f t ( ) From this, we see that: ω n = k m = k 1 k 2 k 1 + k 2 ( ) m and T n = 2 π ω n = 2 π k 1 + k 2 ( ) m k 1 k 2 For k 2 = k 1 , we have: ω n = k 1 2 m = 1600 N / m 2 2 kg ( ) = 20 rad / sec and T n = 2 π ω n = 2 π 20 = 0.314 sec For f t ( ) = I δ ( t )...
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hwk11_soln - Problem 11.1 SOLUTION Consider the undamped...

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