A rigid block of mass ? is mounted on four elastic supports, as shown in the figure. A mass ? drops from a height ? and adheres to the rigid block without rebounding. If the spring constant of each elastic support is ?, derive the equation of motion and find the natural frequency of vibration of the system (a) without the mass ?, and (b) with the mass ?. Also, find the resulting motion of the system in case (b). By using lagrange energy method

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A:

Q: 1. A machine component of mass 0.77 kg moves with SHM in a straight line and completes 175…

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A:

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A:

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Q: For the system shown below, the disc of mass M rolls without slip. Assume that the mass M - 11 kg,…

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Q: factory machine with a mass of 320 kg vibrations up and down with  frequency of 8 Hz. Amplitude of…

A: For solution refer below images.

Q: Q2. Derive the equation of motion and find the natural frequency of vibration of the system shown in…

A: 7

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Q: Figure below shows a rod with mass M = 100 kg, cross section area A = 10 cm². The rod is supported…

A: According to the question data provided in the question M=100kg m=120kg A=10cm2=0.001m2 L=1m f=180Hz…

Free undamped vibrations

Whenever an object/system displaces in either side of its equilibrium position with the help of an external/internal means, then the object/system moves regularly or randomly on both sides of its equilibrium position. This motion is called vibration. Generally, there are three types of vibration: longitudinal vibration, transverse vibration, and torsional vibration.