The amplitude of a spring oscillator decreases by 50% after 1 period. What is tgr amplitude after 3 oscillations? What is the time constant assuming that one period is 2seconds?

Answer 1

When the amplidtude is 1/e...1/e=.3676

A=(1/2)^periods=
and then .5^periods=1/e
take ln of each side
periods *ln.5=-1
periods=-1/ln(.5)=1.44
so time constant is1.44*1=2.88seconds