Question

a simple hormonic oscillator has time period T. the time taken by it to travel from the extreme position to half the amplitude is:

Answer 1

a simple hormonic oscillator has time period T. the time taken by it to travel from the extreme position to half the amplitude is: T/6

Answer 2

On starting from mean position, the equation for displacement is x=Asin(wt). However, starting from the right extreme, the equation is x=Acos(wt). This is because the angle changes by π/2 as we go from mean to extreme. If we see SHM as a form of circular motion, sin(π/2+x)=cos (x). Hence, the time taken changes in the two cases.