Quiz1-Solution-F2020_1

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Oct 30, 2023

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Quiz#1 Solution If your last digit of your student number lands on an odd number use Version A and if it lands on an even number use Version B. Quiz#1 Version A Use Newton’s 2 nd law, or conservation of energy to Find the equation of motion [6%] and natural frequency [2.5%] for the shown system. If the system is excited only due to an initial displacement, ! " , of the mass, explain how natural frequency of the system will be changed if ! " is increased [1.5%]. Note : Assume the system is a rigid pendulum with end mass m that is constrained in planar motion by a linear spring of constant k . The spring is unreformed when the pendulum is vertical ( ! = 0) . Assume ! is small and neglect the mass of the bar. Solution
Quiz#1 Solution Quiz#1 Version B Use Newton’s 2 nd law, or conservation of energy to Find the equation of motion [6%] and natural frequency [2.5%] for the shown system. If the system is excited only due to an initial displacement, ! " , of the mass, explain how natural frequency of the system will be changed if ! " is increased [1.5%]. Note : Assume the system is a rigid pendulum that is constrained in planar motion by a spring of constant k at halfway of its length. The pendulum has two lumped masses m 1 , and m 2 as shown in the figure. The spring is unreformed when the pendulum is vertical ( ! = 0) . Assume ! is small and neglect the mass of the bar. Solution
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