# What is the speed of an oscillating body weighing 3 kg when it is displaced from the equilibrium

What is the speed of an oscillating body weighing 3 kg when it is displaced from the equilibrium position by 3 cm, if the stiffness of the spring is 120,000 N / m, and its speed in the equilibrium position is 10 m / s?

Given:
m = 3kg,
x = 3cm = 0.03m,
k = 120000N / m,
V0 = 10m / s;
Find: V -?
Let’s apply the law of conservation of energy. When the body passes through the equilibrium point, the system has only the kinetic energy of the body:
E = 1/2 * m * (V0) ^ 2 = 1/2 * 3 * 100 = 150J;
When the body is in an intermediate position, the system has the kinetic energy of the body and the potential energy of the spring:
E = Ek + Ep;
Spring potential energy:
Ep = 1/2 * k * x ^ 2 = 1/2 * 120000 * 0.03 ^ 2 = 54J;
Ek = 1/2 * m * V ^ 2;
We find the kinetic energy of the body:
Ek = E – Ep = 96J;
1/2 * m * V ^ 2 = 96J;
V = 8m / s.

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