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A 1 kg block attached to a spring vibrates with a frequency of 1 Hz on a frictionless horizontal table. Two springs identical to the original spring are attached in parallel to an 8 kg block placed on the same table. So, the frequency of vibration of the 8 kg block is?
Most Upvoted Answer
A 1 kg block attached to a spring vibrates with a frequency of 1 Hz on...

Analysis:

The frequency of vibration of a block attached to a spring is given by the formula:

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

where
- \( f \) is the frequency of vibration
- \( k \) is the spring constant
- \( m \) is the mass of the block

Given:

For the 1 kg block:
- \( m = 1 \, \text{kg} \)
- \( f = 1 \, \text{Hz} \)

Calculations:
The spring constant for the 1 kg block can be found using the given frequency:

\[ 1 = \frac{1}{2\pi} \sqrt{\frac{k}{1}} \]
\[ k = 4\pi^2 \, \text{N/m} \]

Frequency for the 8 kg block:
When two identical springs are attached in parallel, the effective spring constant is the sum of the individual spring constants:

\[ k_{\text{total}} = 2k = 8\pi^2 \, \text{N/m} \]

For the 8 kg block:
- \( m = 8 \, \text{kg} \)

Using the formula for frequency of vibration:

\[ f' = \frac{1}{2\pi} \sqrt{\frac{k_{\text{total}}}{m}} \]
\[ f' = \frac{1}{2\pi} \sqrt{\frac{8\pi^2}{8}} \]
\[ f' = \frac{1}{2\pi} \sqrt{\pi^2} \]
\[ f' = \frac{1}{2\pi} \pi \]
\[ f' = 0.5 \, \text{Hz} \]

Therefore, the frequency of vibration of the 8 kg block will be 0.5 Hz when attached to two springs in parallel.
Community Answer
A 1 kg block attached to a spring vibrates with a frequency of 1 Hz on...
F=1/4 hz
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A 1 kg block attached to a spring vibrates with a frequency of 1 Hz on a frictionless horizontal table. Two springs identical to the original spring are attached in parallel to an 8 kg block placed on the same table. So, the frequency of vibration of the 8 kg block is?
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A 1 kg block attached to a spring vibrates with a frequency of 1 Hz on a frictionless horizontal table. Two springs identical to the original spring are attached in parallel to an 8 kg block placed on the same table. So, the frequency of vibration of the 8 kg block is? for Class 11 2024 is part of Class 11 preparation. The Question and answers have been prepared according to the Class 11 exam syllabus. Information about A 1 kg block attached to a spring vibrates with a frequency of 1 Hz on a frictionless horizontal table. Two springs identical to the original spring are attached in parallel to an 8 kg block placed on the same table. So, the frequency of vibration of the 8 kg block is? covers all topics & solutions for Class 11 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for A 1 kg block attached to a spring vibrates with a frequency of 1 Hz on a frictionless horizontal table. Two springs identical to the original spring are attached in parallel to an 8 kg block placed on the same table. So, the frequency of vibration of the 8 kg block is?.
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