Calculating Frequency of Vertical Oscillation for a Spring-Mass System

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To calculate the frequency of a spring-mass system, the maximum acceleration is given by the equation a(max) = -w^2 * A, where A represents the amplitude of oscillation. In this case, the block oscillates with a maximum displacement of 0.091 m below its initial position, leading to an amplitude of 0.0455 m. The angular frequency (w) is derived from the maximum acceleration, resulting in w^2 = 108, which gives a frequency (f) of approximately 1.65 Hz. The discussion emphasizes the importance of accurately determining the amplitude as half the distance between the highest and lowest points of oscillation. Understanding these calculations is crucial for analyzing the motion of the spring-mass system.
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Homework Statement


A spring is suspended from a ceiling and has a block attached to its lower end. The block is held a distance y1 from the ceiling (at this point the spring is at its rest length) and released. The block oscillates up and down with its lowest point being 0.091 m below y1. Find the frequency of the motion.


Homework Equations


a(max) = -w^2 *A
y(t) = A cos (wt + phi)

The Attempt at a Solution


a(max) = -w^2*A = -9.8
w^2 = 108
f = 1.65 /s


Someone please help
 
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The block oscillates between the highest and lowest points but the amplitude is half of the distance between them.

ehild
 

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