Finding acceleration, velocity, and time for simple harmonic motion

[andreaumali]

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. v_x,max=ωA

iii. a_x,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. v_max=.961m/s; a_max=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?

 

[climb515c]

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.