sinusoidal output using servo motor

Hi guys.
I wanna produce a sinusoidal rotating motion using a servo motor.
and then i want to change the reversing rotation - output of servo motor - to a sinusoidal linear motion using a ball screw.
but the problem is the desirable frequency. i must have a sinusoidal linear motion with frequency about 15 Hz. can a servo motor produce an output for this purpose ?
I mean can a servo motor reverse its rotating direction each 0.03 second ?

Yes, but you'll be limited by the total angular momentum and linear momentum in the system.

The equations are simple, force = rate of change of linear momentum (I dv/dt)
torque = rate of change of angular momentum (L dw/dt)

Rates of change go up with the frequency for fixed amplitude and 15Hz is pretty high...