Calculating Bullet Speed Before Impact for Vibration Problem

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To calculate the bullet's speed before impact, the initial kinetic energy of the bullet must equal the potential energy stored in the spring after the impact. The spring's potential energy can be calculated using the formula PE = 0.5 * k * x^2, where k is the spring constant and x is the amplitude. Given the mass of the bullet and block, the bullet's speed can be derived from the conservation of momentum, as both objects move together post-impact. Energy conservation principles indicate that the initial kinetic energy of the bullet is transformed into the spring's potential energy and kinetic energy of the combined mass. Thus, solving these equations will yield the bullet's speed before impact.
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A 20.0 g bullet strikes a 0.600 kg block attached to a fixed horizontal spring whose spring constant is 6.74 103 N/m and sets it into vibration with an amplitude of 21.2 cm. What was the speed of the bullet before impact if the two objects move together after impact?

I've been stuck on this question for days! help please!
 
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For the block+bullet -system to oscillate with the given amplitude, what must the (initial kinetic) energy of the system be?

During impact energy is not conserved, though.
 

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