Derive the equation of the resonance frequency of the unifor

Derive the equation of the resonance frequency of the uniform cantilever beam shown below by using method of conservation of energy. [Solution tips: U_max. maximum strain energy is equal to max. kinetic energy of vibrating body.] T_max = 1/2 integral^1_0 y^2m dx U = 1/2 integral^1_0 M(x)^2/EI dx

Solution

by solving the above two formulae

the maxmum kinetic energy for the cantilever beam is

maximum kinetic energy=0.5*m(frequency)²

maximum strain energy=0.5((3EI)/L³)A²

by eqauting both and by solving both we will get

resonance energy as = sqrt(3EI/mL³)