Question

Как изменится частота колебаний тела, подвешенного на пружине, при увеличении его массы в 4 раза?

Answer 1

Период увеличится в 2 раза
частота уменьшится в 2 раза

Answer 2

Change in Frequency of Oscillation

When a body is suspended on a spring, the frequency of its oscillation changes when its mass is increased. The relationship between the frequency of oscillation and the mass of the body can be described using the formula:

f = (1/2π) * √(k/m)

Where: - f represents the frequency of oscillation, - k is the spring constant, and - m is the mass of the body.

Effect of Increasing Mass by 4 Times

When the mass of the body suspended on the spring is increased by 4 times, the frequency of oscillation will change. According to the formula, the frequency of oscillation is inversely proportional to the square root of the mass. Therefore, when the mass is increased, the frequency of oscillation will decrease.

Calculation

Using the formula f = (1/2π) * √(k/m), if the mass is increased by 4 times, the new frequency (f') can be calculated as follows:

f' = (1/2π) * √(k/(4m))

This shows that the frequency of oscillation will decrease as the mass increases.

Conclusion

Therefore, when the mass of a body suspended on a spring is increased by 4 times, the frequency of its oscillation will decrease.