A load with a mass of m = 3 kg vibrates on a spring with a stiffness of k = 400N / m with an amplitude of A = 2cm.

A load with a mass of m = 3 kg vibrates on a spring with a stiffness of k = 400N / m with an amplitude of A = 2cm. Find the speed v of the load passing the point with the coordinate x = 1 cm.

The total mechanical energy is equal to the sum of the kinetic and potential energies:
E = Ek + Ep;
E = k A ^ 2/2 = 400 2 ^ 2 / (2 10 ^ 4) = 0.08 J;
Ep = k x ^ 2/2 = 400 1 ^ 2 / (2 10 ^ 4) = 0.02 J, where x is the coordinate of the point;
Еk = E – Ep = 0.08 – 0.02 = 0.06 J;
1 J = 1 N m = 1 kg m ^ 2 / sec ^ 2;
Body kinetic energy formula:
Ek = mv ^ 2/2;
v = √2Ek / m = √ (2 0.06 / 3) = 0.2 m / s.
Answer: The speed v of the load passing the point with the coordinate x = 1 cm is equal to 0.2 m / sec.