Please help with F. I\'ve got all the other answers I\'m just completely stuck o

Question

Please help with F. I've got all the other answers I'm just completely stuck on the last one, F. Thanks!

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 1.60 cm, and the frequency is 2.10 Hz

A: Find an expression for the position of the particle as a function of time. (Use the following as necessary: t, and .) ~ 1.6sin(2*2.10*pi*t)

B: Determine the maximum speed of the particle. ~ 21.11

C: Determine the earliest time (t > 0) at which the particle has this speed ~ .2381

D: Find the maximum positive acceleration of the particle. ~ 278.560

E: Find the earliest time (t > 0) at which the particle has this acceleration. ~ .35714

F: Determine the total distance traveled between t = 0 and t = 0.71 s ~The correct answer is for sure between 8 and 9 cm because that's what my professor said, but I'm confused on how to work out the problem

Explanation / Answer

part F :

for simple harmonic motion

x i = Asinwt

Here w = 2*pi*f

given f = 2.10 Hz

W = 2*3.14* 2.1

W = 13.188 rad/s

A = 0.016 m

(x )t = 0 = 0

(x )t =0.94

x(t) = 0.016*sinw*0.71

x(t) = 0.016 * sin (13.188 *0.71)

x(t) = 0.98 mm

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