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# GATE 2022 ME: Theory of Machines Quiz - 7

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Question 1

The natural frequency of the system in cycles/s is Question 2

The string, the spring and the pulley shown in figure are light. The time period of the mass m? Question 3

The spring mass system shown below has mass m=3 kg and the stiffness of the spring is k=20 kN/m. The natural frequency of the system in Hz (rounded to the nearest integer) is _______. Question 4

A 1m long cantilever beam carrier a mass of 20 kg at the free end. If the second moment of area and Young’s modulus are 300 mm4 and 300 GPa respectively, the natural frequency of the system will be

Question 5

A solid disc with radius a is connected to a spring at a point d above the center of the disc. The other end of the spring is fixed to the vertical wall. The disc is free to roll without slipping on the ground. The mass of the disc is M and the spring constant is K. The polar moment of inertia for the disc about its centre is J = Ma2/2. The natural frequency of this system in rad/s is given by

Question 6

A machine part of mass 2 kg vibrates in viscous medium, angular frequency at resonance condition is found to be 10π rad/s. If a harmonic exciting force of 25 N produces 1.25 cm. Find the stiffness of the system in N/m.
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