(Solved): A particle moving along the \( x \) axis in simple harmonic motion starts from its equilibrium pos ...

A particle moving along the \( x \) axis in simple harmonic motion starts from its equilibrium position, the origin, at \( t=0 \) and moves to the right. The amplitude of its motion is \( 2.00 \mathrm{~cm} \), and the frequency is \( 1.50 \mathrm{~Hz} \). (a) Find an expression for the position of the particle as a function of time. Determine (b) the maximum speed of the particle and (c) the earliest time \( (t>0) \) at which the particle has this speed. Find (d) the maximum positive acceleration of the particle and (e) the earliest time \( (t>0) \) at which the particle has this acceleration. (f) Find the total distance traveled by the particle between \( t=0 \) and \( t=1.00 \mathrm{~s} \).