Total ME of 2kg Oscillating on 50 N/m Spring

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The total mechanical energy of a 2 kg mass oscillating on a spring with a spring constant of 50 N/m and a maximum velocity of 5 m/s is calculated using the formula E = (1/2)mv^2 + (1/2)kx^2. At the equilibrium position, where the spring's displacement is zero, the energy simplifies to E = (1/2)(2 kg)(5 m/s)^2, resulting in a total mechanical energy of 25 Joules. This calculation highlights the relationship between kinetic energy and potential energy in oscillatory motion.
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What is the total mechanical energy of a mass of 2 kg oscillating on a spring given that the maximum velocity of the mass is 5 m/s and the spring constant is 50 N/m?
 
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The formula for mechanical energy is this:
E = (1/2)mv^2 + (1/2)kx^2

When the mass is at the equilibrium position, the spring is 0 from equilibrium and the mass is at maximum velocity. The formula looks like this then
E = (1/2)(2)(5)^2 + (1/2)(50)(0)^2
E = 25 Joules

Wasn't that easy :)
 

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