Question

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. Find m.

Answer 1

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,

                                          $T=2\pi \sqrt{\frac{m}{k} }$

• Where, m is the mass of the body and k is the spring constant.

How to solve the problem?

• Given that,

               $T_1=2s\\m_1=m\\m_2=m+2kg\\T_2=3s$

• We have to find the value of m,

              $T_1=2\pi \sqrt{\frac{m}{k} } \\T_2=2\pi \sqrt{\frac{m+2}{k} } \\\frac{T_1}{T_2} =\sqrt{\frac{m}{m+2} }\\\frac{2}{3} =\sqrt{\frac{m}{m+2} }$

               $m=\frac{5}{8} =0.625kg$

Thus, we can conclude that, the mass m will be 0.625kg.

Learn more about simple harmonic motion here:

brainly.com/question/28045110

#SPJ4