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**[SOLVED] Simple Harmonic Motion**

**1. Homework Statement**

A cheerleader waves her pom-pom in simple harmonic motion with an amplitude of 18.0 cm and a frequency of 0.850 Hz. Find (a) the maximum magnitude of the acceleration and of the velocity; (b) the acceleration and speed when the pom-pom's coordinate is x = +9.0 cm; (c) the time required to move from the equilibrium position directly to a point 12.0 cm away. (d) Which of the quantities asked for in parts (a), (b), and (c) can be found using the energy approach, and which ones cannot? Explain.

**2. Homework Equations**

abs(a_max)= ω^2A, A = amplitude

abs(v_max)=ωA

ω=2πf, f=frequency

a = -ω^2 sqrt(A^2 - x^2)

**3. The Attempt at a Solution**

(a) ω=2π(0.85)= 5.34 rad/s

abs(a_max)= (5.34)^2(0.18)= 5.13m/s^2

abs(v_max)= (5.34)(0.18) = 0.961 m/s

(b) a = -(5.34)^2 sqrt((0.18)^2 - (0.09)^2) = -4.45m/s^2

speed = abs(v) = (5.34) sqrt((0.18)^2 - (0.09)^2) = 0.832 m/s

I don't know how to approach (c) and (d).