Question

Determine the equation of motion and natural frequency of the system by the newtons method mechanical vibration lasithan book

Answer 1

Bold notion indicates that the variable is a vector. This equation correlates to the physical embodiment of a force of 1 N equivalent to a mass of 1 kg accelerating at 1 m/sec^2

By manipulating this equation we can bring forth other useful gravitational relationships. Earlier in this chapter Inertia was briefly mentioned as the property of matter which acts as a resistance to a change in the bodies momentum; this is explained as a body which has a mass m having a change in velocity. The change in momentum per unit time is related to the acceleration of the body and is represented equationally by:



{\displaystyle \mathbf {p} =m\mathbf {v} } {\displaystyle \mathbf {p} =m\mathbf {v} }


{\displaystyle \ \sum {\mathbf {F} }={\mathrm {d} \mathbf {p} \over \mathrm {d} t}=m{\mathrm {d} \mathbf {v} \over \mathrm {d} t}=m\mathbf {a} } {\displaystyle \ \sum {\mathbf {F} }={\mathrm {d} \mathbf {p} \over \mathrm {d} t}=m{\mathrm {d} \mathbf {v} \over \mathrm {d} t}=m\mathbf {a} }

This can be seen as a direct relation to Newton's Second Law of Motion in the experiment of Hooke's Law;



{\displaystyle \mathbf {F} =m\mathbf {a} } {\displaystyle \mathbf {F} =m\mathbf {a} }


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