Question

Груз подвешенный на пружине совершает свободные колебания между точками 1 и 3. в каком положении груза его кинетическая энергия максимальна?

Answer 1

Кинетическая энергия будет максимальной в промежуточном положении 2 ровно посередине между 1 и 3 т.к. в этой точке скорость груза будет наибольшей

Answer 2

Position of Maximum Kinetic Energy in Simple Harmonic Motion

In a simple harmonic motion, the position where the kinetic energy of the mass is maximum can be determined. The kinetic energy of the mass in simple harmonic motion is maximum when the displacement is at its maximum value.

The displacement of the mass in simple harmonic motion is given by the equation:

x(t) = A * cos(ωt + φ)

Where: - x(t) is the displacement at time t - A is the amplitude of the motion - ω is the angular frequency - φ is the phase angle

The kinetic energy of the mass in simple harmonic motion is given by the equation:

KE = (1/2) * m * v^2

Where: - KE is the kinetic energy - m is the mass - v is the velocity

From the equation for displacement, it can be observed that the displacement is maximum when the cosine function is at its maximum value, which is 1. Therefore, the kinetic energy is maximum when the displacement is maximum, i.e., at the extreme points of the motion (points 1 and 3).

Therefore, the kinetic energy of the mass is maximum at points 1 and 3.