Will a SHM eventually reach zero displacement or not?

[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 wouldn't they?

 

[mgb_phys]

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.

 

[linyen416]

mgb,
thanks for ur input!

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

 

[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.