Question

Найти массу груза, подвешенного к пружине, если он за 10 секунд совершает 20 колебаний. Жесткость пружины 20 нм. распишите пожалуйста​

Answer 1

Ответ:

Дано:

t = 10с.

T = 20кол.

k =20Н/м

Найти: m -?

Решение:

T=2П√m/k => m=k(T/2П)²

T=10с/20кол=0,5с.

m=20H/м*(0,5с/2*3,14)²≈1кг

Ответ: m ≈1кг

Answer 2

Calculating the Mass of the Load Suspended from a Spring

To calculate the mass of the load suspended from a spring, we can use the formula for the period of oscillation of a mass-spring system:

Period of oscillation (T) = 2π√(m/k)

Where: - T = period of oscillation - m = mass of the load - k = stiffness of the spring

Given: - Period of oscillation (T) = 10 seconds - Number of oscillations (n) = 20 - Stiffness of the spring (k) = 20 N/m

First, let's calculate the frequency of oscillation using the given period: Frequency (f) = 1 / T

Frequency (f) = 1 / 10 Frequency (f) = 0.1 Hz

Now, we can calculate the angular frequency (ω) using the frequency: Angular frequency (ω) = 2πf

Angular frequency (ω) = 2π * 0.1 Angular frequency (ω) = 0.2π rad/s

Next, we can calculate the mass of the load using the formula for the period of oscillation: Period of oscillation (T) = 2π√(m/k)

Given that the load completes 20 oscillations in 10 seconds, we can find the period of one oscillation: Period of one oscillation (T') = T / n

Period of one oscillation (T') = 10 / 20 Period of one oscillation (T') = 0.5 seconds

Now, we can use the period of one oscillation to calculate the mass of the load: T' = 2π√(m/k)

Solving for m: m = (T' * k) / (2π)^2

Substitute the values: m = (0.5 * 20) / (2π)^2 m ≈ 0.397 kg

So, the mass of the load suspended from the spring is approximately 0.397 kg.