https://file.aiquickdraw.com/mathbot/file/1726848803937vmhnxike.jpg

The problem in the image involves calculating the new frequency of oscillations of a spring pendulum when the mass of the load is increased.

The given parameters are:
- Initial frequency of small vertical oscillations of a spring pendulum: \( f_1 = 6 \, \text{Hz} \)
- The mass of the load is increased by a factor of 4.

The frequency of oscillations for a spring pendulum is given by the formula:

\[
f = \frac{1}{2\pi} \sqrt{\frac{k}{m}}
\]

Where:
- \( f \) is the frequency,
- \( k \) is the spring constant,
- \( m \) is the mass of the load.

From this, we can see that the frequency is inversely proportional to the square root of the mass:

\[
f \propto \frac{1}{\sqrt{m}}
\]

When the mass is increased by a factor of 4, the new frequency \( f_2 \) will be:

\[
f_2 = f_1 \cdot \frac{1}{\sqrt{4}} = f_1 \cdot \frac{1}{2}
\]

Now, substituting the given initial frequency \( f_1 = 6 \, \text{Hz} \):

\[
f_2 = 6 \, \text{Hz} \times \frac{1}{2} = 3 \, \text{Hz}
\]

Thus, the new frequency will be **3 Hz**.

Would you like more details, or do you have any questions?

Here are 5 related questions to explore further:
1. How would the frequency change if the mass is doubled instead of quadrupled?
2. What effect would increasing the spring constant \( k \) have on the frequency?
3. How is the period of oscillations related to the frequency for a spring pendulum?
4. What is the formula for the potential energy stored in a spring at maximum displacement?
5. Can we derive the equation for frequency from the equation of motion for harmonic oscillators?

**Tip:** The square root dependence of frequency on mass or spring constant is a key characteristic of simple harmonic motion.

Частота собственных малых вертикальных колебаний пружинного маятника равна 6 Гц. Какой станет частота таких колебаний, если массу груза пружинного маятника увеличить в 4 раза? Ответ приведите в герцах.

Calculate the new frequency of a spring pendulum when the mass of the load is increased by a factor of 4. The initial frequency is 6 Hz, and the relationship between frequency and mass in simple harmonic motion is explored. Suitable for high school physics students.

Math Problem Statement

Solution

Ask a new question for Free

By Image

Math Problem Analysis

Mathematical Concepts

Formulas

Theorems

Suitable Grade Level

Related Recommendation