A bead, mass m, is sliding is sliding on a wire which is hanging freely in the shape of a cosh (hyperbolic cos) function. Assume the bead moves with no friction. For very small displacements in x what is the frequency of oscillation. You may use for the height of the wire and thus the height of the bead as a function of x the Taylor series expansion for cosh H(r) = 1+r/2 + x*/24 + ..

A bead, mass m, is sliding is sliding on a wire which is hanging freely in the shape of a cosh (hyperbolic cos) function. Assume the bead moves with no friction. For very small displacements in x what is the frequency of oscillation. You may use for the height of the wire and thus the height of the bead as a function of x the Taylor series expansion for cosh H(r) = 1+r/2 + x*/24 + ..