How Is Amplitude and Total Energy Calculated in a Spring System?

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To calculate the amplitude of oscillation in a spring system with a mass of 0.5 kg and a spring constant of 0.40 N/m, the equation x = A cos(wt) is relevant. The speed of the mass at 0.7 seconds is 1.75 m/s, indicating that energy conservation principles apply. The total energy in the system can be derived from the kinetic and potential energy equations, considering the mass's position and velocity. Users in the discussion emphasize the need to apply conservation of energy to find both the amplitude and total energy accurately. The problem requires a clear understanding of harmonic motion and energy transformations in spring systems.
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A mass of 0.5 kg is attached to the end of a massless spring of spring constant 0.40 N/m. It is released from rest from an extended position. After 0.7 s, the speed of the mass is measured to be 1.75 m/s. What is the amplitude of oscillation? What is the total energy (relative to the mass at rest in the unextended position) contained in this system?



x=Acoswt
conservation of energy



I've tried many different attempts.
 
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Anyone have any help on this problem. I think I have to use conservation of energy but I really am not sure
 

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