Question

Амплитуда колебаний груза на пружине равна 3см. Какой путь положения равновесия пройдет груз на 1/4Т ; 1/2Т ; 3/4Т ; Т.(Не только ответы а плиз с решением)

Answer 1

за 1/4 = 3 см, за 1/2 6 см, за 3/4 = 9 см,  за т 12 см

Answer 2

Amplitude of Oscillations and Equilibrium Position

The amplitude of oscillations of a mass on a spring is the maximum displacement from the equilibrium position. In this case, the amplitude of the oscillations is given as 3 cm.

To find the displacement of the mass at different times, we can use the equation for simple harmonic motion:

x(t) = A * cos(ωt + φ)

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

In this case, we are given the amplitude as 3 cm. To find the angular frequency, we can use the formula:

ω = 2π / T

Where: - T is the period of the oscillations

Let's calculate the displacement of the mass at different times:

At 1/4T:

To find the displacement at 1/4T, we need to substitute t = 1/4T into the equation for simple harmonic motion:

x(1/4T) = A * cos(ω * (1/4T) + φ)

Since we know the amplitude is 3 cm, we can substitute A = 3 into the equation:

x(1/4T) = 3 * cos(ω * (1/4T) + φ)

To find the value of ω, we can use the formula ω = 2π / T. However, we are not given the period T in this case. Without the value of T, we cannot calculate the displacement at 1/4T, 1/2T, 3/4T, and T accurately.

Please provide the value of the period T so that we can continue with the calculations.