A particle executes simple harmonic motion with a time period of 16s. At time `t=4s` its velocity is `4ms^(-1)`. Find its amplitute of motion.

Explanation

Here, `T=16s,At t=2s, y=0`
and at `t=4s,V=4ms^(-1), a=?`
For simple harmonic motion,
`y=asinomegat =asin((2pi)/(T))t`
When `t=4s`, the time taken by particle to travel from the mean position to a given position `=4-2=2s. ` The displacement,
`y=asin((2pi)/(16)xx2)=asin((pi)/(4))=(a)/(sqrt2)` ...(i)
Velocity, `V=omegasqrt(a^(2)-y^(2))` ,brgt `:. 4=((2pi)/(16))sqrt(a^(2)-a^(2)//2)=(pi)/(8)xx(a)/(sqrt(2))`
or `a=(32sqrt(2))/(pi)=14.4m`