Solving Vibrations and Waves: Mass, Spring Constant, Energy, Speed

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A 5 kg mass attached to a spring with a spring constant of 13 N/cm, pulled back 20 cm, has a total energy of 26 joules at the moment of release. The energy is calculated using the potential energy formula, where kinetic energy is zero at the point of release. For the second scenario with a 15 kg mass and a spring constant of 20 N/cm, the speed at 5 cm is sought, with the answer indicated as 2.2 m/s. The discussion emphasizes the importance of understanding energy storage in springs and the relationship between mass, spring constant, and speed. The problem-solving approach highlights the need for clarity in energy calculations at different points in the spring's motion.
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1) A 5 kg mass, m, rests on a frictionless, horizontal, wooden table top, and is attached to one end of a spring anchored at its other end . If the spring has a spring constant=13 N/cm and the mass is pulled back (in the positive direction ) 20 cm and released, to the nearest tenth of a joule, what is its total energy?
2) if the mass is 15 kg and the spring constant is 20 N/cm, to the nearest tenth of a m/s, what is its speed at x= 5 cm?

I have solved the 1st one :

1N/cm=100N/m

E = PE + KE
E = 1/2kA^2 + 1/2mv^2 At KE v=0 because the mass stops momentarily as it changes directions. Then :

E = PE
E = 1/2kA^2
E = 1/2(13*100)*(0.2)^2
E = 26J

I have problem with the second problem. please help to solve this. I have 2 hours that I am tryin to solve it . I have only the answer that is 2.2m/s.

Please help......



:cry: Lol...
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The spring is still pulled back 20 cm in part (b). Can you find how much energy is stored in it at the moment of release when v = 0?
 

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