Answer: The end point of a spring oscillates with a period of 2.0 s when a block with mass m is attached to it. When this mass is increased by 2.0 kg, the period is found to be 3.0 s. Then the mass m is 0.625kg.
Explanation: To find the answer, we need to know more about the simple harmonic motion.
What is simple harmonic motion?
- A particle is said to execute SHM, if it moves to and fro about the mean position under the action of restoring force.
- We have the equation of time period of a SHM as,
[tex]T=2\pi \sqrt{\frac{m}{k} }[/tex]
- Where, m is the mass of the body and k is the spring constant.
How to solve the problem?
[tex]T_1=2s\\m_1=m\\m_2=m+2kg\\T_2=3s[/tex]
- We have to find the value of m,
[tex]T_1=2\pi \sqrt{\frac{m}{k} } \\T_2=2\pi \sqrt{\frac{m+2}{k} } \\\frac{T_1}{T_2} =\sqrt{\frac{m}{m+2} }\\\frac{2}{3} =\sqrt{\frac{m}{m+2} }\\\\[/tex]
[tex]m=\frac{5}{8} =0.625kg[/tex]
Thus, we can conclude that, the mass m will be 0.625kg.
Learn more about simple harmonic motion here:
https://brainly.com/question/28045110
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