# SHM question

1. Aug 22, 2008

### linyen416

THEORETICALLY will a SHM eventually reach zero displacemtn or not?

If it is DAMPED, amplitude would decrease with time, as would frequency, but would they would reach zero wouldnt they?

Last edited by a moderator: Aug 23, 2008
2. Aug 22, 2008

### mgb_phys

Re: [Something descriptive here will yield more responses]

In the real world with friction and energy lost to the surrounding, yes it will reach zero displacement. Or rather it will reach a point where the random thermal motion is the same as the background.
In simple physics models you assume the loss in energy is proportional to the displacement and so in theory it would never reach zero. In the same way that a theoretical cup of coffee would never cool down to room temperature - because cooling rate is proportional to the temperature difference.

3. Aug 23, 2008

### linyen416

Re: [Something descriptive here will yield more responses]

mgb,
thanks for ur input!

im wondering about underdamped oscillation as well. would displacement theoretically ONLY APPROACH zero?

4. Aug 23, 2008

### baltimorax

Hi,

in an underdamped shm, the motion decreases by the factor e^(-kt), where k is the frictional force and t is time. as this is a decreasing exponential it will never techniquelly reach zero.