A precision instrument package (m = 1kg) needs to be mounted on a surface vibrating at 60 Hz. It is desired that only 5% of the base surface vibration amplitude be transmitted to the instrument. Assume that the isolation is designed with its natural frequency significantly lesser than 60Hz, so that the effect of damping may be ignored. The stiffness (in N/m) of the required mounting pad is _____________.

Figure shows a single degree of freedom system. The system consists of a mass less rigid bar $$OP$$ hinged at $$O$$ and a mass $$m$$ at end $$P.$$ The natural frequency of vibration of the system is

Consider a cantilever beam, having negligible mass and uniform flexural rigidity, with length $$0.01m$$. The frequency of vibration of the beam, with a $$0.5$$ kg mass attached at the free tip, is $$100Hz$$. The flexural rigidity (in $$N.{m^2}$$) of the beam is _________.

A rigid uniform rod $$AB$$ of length $$L$$ and mass $$m$$ is hinged at $$C$$ such that $$AC = L/3, CB = 2L/3.$$ Ends $$A$$ and $$B$$ are supported by springs of spring constant $$k.$$ The natural frequency of the system is given by