Simple harmonic motion with an amplitude

AI Thread Summary
The discussion focuses on solving a physics problem involving simple harmonic motion, where a block attached to a spring with a spring constant of 5.50 N/m has an amplitude of 12.5 cm and a measured speed of 25.0 cm/s at a specific point. Participants suggest using conservation of energy principles to find the mass of the block, proposing the equation 1/2 kA^2 = 1/2 mv^2 as a method to relate kinetic and potential energy. There is confusion regarding the correct application of formulas, particularly in deriving the mass from the given parameters. The conversation emphasizes the importance of showing calculations to identify mistakes in the approach. The thread ultimately seeks clarity on applying energy conservation to solve for the mass, period, and maximum acceleration of the block.
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Homework Statement


A block of unknown mass is attached to a spring with a spring constant of 5.50 N/m and undergoes simple harmonic motion with an amplitude of 12.5 cm. When the block is halfway between its equilibrium position and the end point, its speed is measured to be 25.0 cm/s.

(a) Calculate the mass of the block.
(b) Calculate the period of the motion.
(c) Calculate the maximum acceleration of the block.


Homework Equations


Vmax = sqrt(k/m)A
T= 2pi/w
a_max = kA/m



The Attempt at a Solution


so i thought i would use the first formula i stated to find the mass of the block
but apparently I am wrong.
can someone please help me get started.
thanks
 
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Well the total energy of the system is given by 1/2 kA2 and throughout the motion this is interchanged between elastic potential and kinetic energy. So halfway between the max point and equilibrium, how far does the spring stretch? Can you now apply a conservation of energy to get the mass?
 


Show your calculations to see where you have made mistake.
 


well what i did was
vmax = sqrt(k/m)A
(v^2/A^2)m = k
so
m = kA^2/v^2 but i guess this is wrong

so do i use something like 1/2kA^2 = 1/2mv^2 ?
 

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