Period of Motion: Find Mass 0.85kg Piston's Period of Motion

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The discussion focuses on calculating the period of motion for a piston with a mass of 0.85 kg, modeled as simple harmonic motion. Given the acceleration of 8 m/s² when the piston is 10 cm from the midpoint, the formula a = -(2πf)²x is applied to find the frequency. Participants suggest rearranging the equation to solve for frequency (f) and subsequently determining the period (T) using the relation T = 1/f. The calculated velocity of 1.26 m/s is mentioned, but its necessity for finding the period is questioned. Ultimately, the key objective is to derive the period of the piston's motion based on the provided parameters.
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The movement of a particular piston of mass 0.85kg may be modeled with a simple harmonic. Given that its acceleration is 8m/s when 10cm from the mid position. Find the period of the motion??

I found velocity to = 1.26m/s, but I am not even sure if i need to calculate the velocity.
 
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a=-(2πf)2x

We have a (= 8 m/s)
We know 2π (constant)
And we know x (= 10cm)

Rearrange to find f.

Period = 1/f
 
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