GIVEN as,\(K = \frac{{{F_2} - {F_1}}}{{{L_1} - {L_2}}}\)where, F1 = weight of pan, F2 = total weight of pan and extra mass, L1 = initial length of spring, L2 = final length of springThe un-deformed length of spring is, Deflection of spring due to 2 kg pan + ORIGINAL length of springCalculation:Given:\(k= \frac{{\left( {22 - 2} \right) \times 9.81}}{{\left( {200 - 100} \right) \times {{10}^{ - 3}}}} = 1962~N/m\)Deflection of spring due to 2 kg pan\(\delta= \frac{{2 \times 9.81}}{{1962}} = 0.01~m = 10\;mm\)∴ Unperformed length = 200 + 10= 210 mm

"> GIVEN as,\(K = \frac{{{F_2} - {F_1}}}{{{L_1} - {L_2}}}\)where, F1 = weight of pan, F2 = total weight of pan and extra mass, L1 = initial length of spring, L2 = final length of springThe un-deformed length of spring is, Deflection of spring due to 2 kg pan + ORIGINAL length of springCalculation:Given:\(k= \frac{{\left( {22 - 2} \right) \times 9.81}}{{\left( {200 - 100} \right) \times {{10}^{ - 3}}}} = 1962~N/m\)Deflection of spring due to 2 kg pan\(\delta= \frac{{2 \times 9.81}}{{1962}} = 0.01~m = 10\;mm\)∴ Unperformed length = 200 + 10= 210 mm

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A weighing machine consists of a 2 kg pan resting on a spring having linear characterises. In this condition of resting on the spring, the length of spring is 200 mm. When a 20 kg mass is placed on the pan, the length of the spring becomes 100 mm. The un-deformed length L in mm and the spring stiffness k in N/m are

Mechanical Vibrations Undamped Free Vibration in Mechanical Vibrations . 6 months ago

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Concept:The spring stiffness is GIVEN as,\(K = \frac{{{F_2} - {F_1}}}{{{L_1} - {L_2}}}\)where, F1 = weight of pan, F2 = total weight of pan and extra mass, L1 = initial length of spring, L2 = final length of springThe un-deformed length of spring is, Deflection of spring due to 2 kg pan + ORIGINAL length of springCalculation:Given:\(k= \frac{{\left( {22 - 2} \right) \times 9.81}}{{\left( {200 - 100} \right) \times {{10}^{ - 3}}}} = 1962~N/m\)Deflection of spring due to 2 kg pan\(\delta= \frac{{2 \times 9.81}}{{1962}} = 0.01~m = 10\;mm\)∴ Unperformed length = 200 + 10= 210 mm

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Posted on 10 Nov 2024, this text provides information on Mechanical Vibrations related to Undamped Free Vibration in Mechanical Vibrations. Please note that while accuracy is prioritized, the data presented might not be entirely correct or up-to-date. This information is offered for general knowledge and informational purposes only, and should not be considered as a substitute for professional advice.

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