The equation of motion of a particle executing SHM is expressed by `x=10sin(10t-pi/6)`. Establish an equation to express its velocity and also calculate the magnitude of its maximum acceleration.

Explanation

Given, `x=10sin(10t-pi/6)`
`therefore` Velocity, `v=(dx)/(dt)=10xx10cos(10t-pi/6)`
`=100cos(10t-pi/6)` unit.
Again, acceleration, `a=(dv)/(dt)=-10xx100sin(10t-pi/6)`
`=-1000sin(10t-pi/6)`unit.
Acceleration will be maximum when,
`sin(10t-pi/6)=1`
`therefore` Magnitude of maximum acceleration, `a_(max)=1000` units.