A ball with a mass of m = 10 g performs harmonic oscillations with an amplitude of A = 20 cm

A ball with a mass of m = 10 g performs harmonic oscillations with an amplitude of A = 20 cm and a period of T = 4 s (a spring pendulum). At time tо = 0, the displacement of the ball is equal to х0 = A. Find the kinetic energy Eк1 at time t = 1 s

m = 10 g = 0.01 kg.

T = 4 s.

A = 20 cm = 0.2 m.

t0 = 0 s.

x0 = A.

t = 1 s.

Ek1 -?

The kinetic energy of the body Ek is determined by the formula: Ek = m * V2 / 2, where m is the mass of the ball, V is the speed of the ball.

The oscillation period T is the time of one complete oscillation.

Since the counting of time occurs in the extreme position of the ball, then after a time t = 1 s it will be in the equilibrium position. In the equilibrium position, all potential energy has passed into kinetic energy: Ek1 = En1.

En1 = k * x2 / 2 = k * A2 / 2.

Ek1 = k * A2 / 2.

For a spring pendulum T = 2 * P * √ m / √ k.

k = 4 * P2 * m / T2.

k = 4 * (3.14) 2 * 0.01 kg / (4 s) 2 = 0.025 N / m.

Ek1 = 0.025 N / m * (0.2 m) 2/2 = 0.0005 J.

Answer: the kinetic energy will be Ek1 = 0.0005 J.