# Oscillation (particle movement)

**1. The problem statement, all variables and given/known data**

A particle rotates counterclockwise in a circle

of radius 4.4 m with a constant angular speed

of 11 rad/s. At t = 0, the particle has an x

coordinate of 2.9 m and y > 0 .

Part 1: Determine the x coordinate of the particle velocity

at t = 1.22 s.

Answer in units of m/s

Part 2: Determine the x coordinate of the particle acceleration

at t = 1.22 s.

Answer in units of m/s^{2}

**2. Relevant equations**

x = Acos(wt + d)

where d was found in a previous part of the problem and confirmed correct by the program to be:

d = 0.8511870029

v = -wAsin(wt + d); v_{x} = -wRsin(wt) = -vsin(wt)

a = -w^{2}Acos(wt + d)

Note R and A are interchangeable

**3. The attempt at a solution**

Part 1:

Attempt 1: v = -wAsin(wt + d) = -(4.4 m)sin(11rad/s * 1.22s + 0.8511870029)

v = -4.360544081 m/s

Incorrect

Attempt 2: v_{x} = -wRsin(wt)

v_{x} = -(11rad/s)(4.4m)sin(11 rad/s * 1.22 s) ≈ -36.477666 m/s

v_{x} = -vsin(wt) = (solution from Attempt 1)sin(wt)

v_{x} = -(-4.360544081 m/s)sin(11 rad/s * 1.22 s) ≈ -3.286414681 m/s

Vastly different answers, don’t know if incorrect because I don’t want to get points deducted from score from trying random answers

http://ift.tt/1maA7b4

## Leave a comment