gud question

A particle of mass m moves in the x-y plane, along a symmetric, frictionless, concave curve. The trajectory length along this curve is denoted by s. A uniform gravitational field acts in the negative y-direction. The particle is to move along this curve with simple harmonic motion with angular frequency w, and the angle of displacement of m from the y-axis is not limited to small values. Find the locus of the curve of the motion in terms of the given parameters.