Finding acceleration, velocity, and time for simple harmonic motion

AI Thread Summary
The discussion focuses on calculating key parameters of simple harmonic motion for a cheerleader's pom-pom, including maximum acceleration and velocity, as well as specific values at a given displacement. The maximum velocity was determined to be 0.961 m/s and the maximum acceleration 5.13 m/s². The time to reach a displacement of 0.120 m from equilibrium was calculated to be 7.16 seconds. There is uncertainty regarding the calculation of acceleration and speed at a specific coordinate, with suggestions to use derivatives of the position function. The energy approach's applicability to the quantities calculated is also debated, particularly regarding the relationship between velocity, displacement, and acceleration.
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Homework Statement



A cheerleader waves her pom-pom in simple harmonic motion with an amplitude of .180m and a frequency of .850Hz.

a) Find the maximum magnitude of the acceleration and of the velocity.

b) Find the acceleration and speed when the pom-pom's coordinate is x=+.090m.

c) Find the time required to move from the equilibrium position directly to a point .120m away.

d) Which of the quantities asked for in parts (a), (b), and (c) can be found using the energy approach (E = K + U = 1/2 mv^2 + mgh = 1/2 kA^2) and which cannot? Explain.


Homework Equations



i. x=Asin(ωt)

ii. vx,max=ωA

iii. ax,max=-ω2A

where ω=angular frequency, A=amplitude, x=displacement from equilibrium, t=time

K=1/2 mv^2

U=mgh


The Attempt at a Solution



I was able to calculate (a) using formulas ii and iii. vmax=.961m/s; amax=5.13m/s^2

I was also able to calculate (c) using formula i. x=7.16s

However, I am unsure of how to find (b).

I think (d) is velocity but I'm not sure if from velocity you'd be able to get x and acceleration?
 
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For part b you know ω, A, and x. You should be able to solve for and find t.

I guess one way to solve "b" is by using your equation(i), you can find speed and acceleration by taking the 1st and 2nd derivative wrt t.
 
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