Question

Амплитуда колебаний груза, массой 200 г, закрепленного на пружине жесткостью 200 Н/м, равна 4 см. С какой скоростью груз проходит положение равновесия

Answer 1

x=Asin(wt), где А - амплитуда колебаний.

W=2п/T 

T=2п*корень(m/k)

V=производная x

t = T*4

В конце концов, выводим формулу  V=A/(корень(m/k))

V = 0,04/0,03=1,3

Но мне кажется, что вы допустили опечатку. Если брать К=2000 Н/м, то ответ будет = 4.

Answer 2

Amplitude of Oscillations and Equilibrium Position

The amplitude of oscillations of a mass attached to a spring can be determined using the equation:

A = (m * g) / k

Where: - A is the amplitude of oscillations - m is the mass of the object (in this case, 200 g) - g is the acceleration due to gravity (approximately 9.8 m/s^2) - k is the spring constant (in this case, 200 N/m).

Given that the amplitude of oscillations is 4 cm (or 0.04 m), we can rearrange the equation to solve for the mass:

m = A * k / g

Substituting the given values:

m = 0.04 * 200 / 9.8

Calculating this, we find that the mass of the object is approximately 0.816 kg.

To find the velocity of the mass when it passes through the equilibrium position, we need to consider the conservation of mechanical energy. At the equilibrium position, the potential energy is zero, and all the energy is in the form of kinetic energy.

The kinetic energy of the mass can be calculated using the equation:

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

Where: - KE is the kinetic energy - m is the mass of the object (0.816 kg, as calculated earlier) - v is the velocity of the object at the equilibrium position.

Since the potential energy is zero at the equilibrium position, the total mechanical energy is equal to the kinetic energy:

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

Solving for v:

v = sqrt(2 * E / m)

Substituting the given values:

v = sqrt(2 * 0 / 0.816)

Since the potential energy is zero at the equilibrium position, the velocity of the mass when it passes through the equilibrium position is zero.

Therefore, the velocity of the mass when it passes through the equilibrium position is 0 m/s.