What is the maximum height from the equilibrium position that an oscillating material point with a mass of 2 kg

What is the maximum height from the equilibrium position that an oscillating material point with a mass of 2 kg, raised on a thread, can rise if its total energy is 64 J.

E = 64 J.

m = 2 kg.

g = 9.8 m / s ^ 2.

hmax -?

The total mechanical energy of the body E is the sum of its kinetic Ek energy of motion and the potential energy En of interaction: E = Ek + En.

The potential energy of the body En is determined by the formula: En = m * g * h, where m is the mass of the body, g is the acceleration of gravity, h is the height of the body.

At the moment of the highest height, the body has only potential energy: E = En.

E = m * g * hmax.

hmax = E / m * g.

hmax = 64 J / 2 kg * 9.8 m / s ^ 2 = 3.26 m.

Answer: the maximum height from the equilibrium position of the material point is hmax = 3.26 m.