I am not sure how to do the heavy damping as shown in the tab below. I am learning on an acoustic guitar, just putting light pressure on the strings kills the sound and makes a odd noise. How do I do the dampening they indicate?

e|--2-------x---------------|-----------------5-------|
B|--1-------x-------3-----3-|-5-------3---------------|
G|--2-------x---------------|-------------------------|
D|--0-------x---------------|-------------------------|
A|--0-------x---------------|-------------------------|
E|--------------------------|-------------------------|

x - play 'note' with heavy damping