Need help please servo motors and steppers or just anything please

hi guys im new here and new to this whole robot world, i have a project going and need help i need the easiest and cheapest, cheap cheap way to do so, im looking for some type of motor or actuator that will go back and forth with a rod, the forward motion needs to be slower than the backwards motion, kinda like a shaking motion. this will all be on a small scale model, it will be moving no more than 5 lbs. pulleys,and cranks are not for me. im just experimenting so i really don’t want to spend much at all. thanks for all your help

Can you describe or draw the project? Having difficulty picturing it. Also, how do you want to control the motor?