A mass m suspended at the end of spring of spring constant k and oscillate at periodic time T. If spring is cut into two part of equal length and tow pails are now connected in parallel and a block is suspended at the end of the combined spring and oscillate then find new periodic time.

A mass m suspended at the end of spring of spring constant k and oscil

1.	A mass m suspended at the end of spring of spring constant k and oscillate at periodic time T. If spring is cut into two part of equal length and tow pails are now connected in parallel and a block is suspended at the end of the combined spring and oscillate then find new periodic time.
Answer» <html><body><p>`2T`<br/>`T`<br/>`(T)/(sqrt(2))`<br/>`(T)/(2)`</p>Solution :`T propto (1)/(sqrt(k))` <br/> The effective force constant in parallel combination of <a href="https://interviewquestions.tuteehub.com/tag/spring-11487" style="font-weight:bold;" target="_blank" title="Click to know more about SPRING">SPRING</a> when spring is divided into two equal parts <br/> `k_(2)= <a href="https://interviewquestions.tuteehub.com/tag/2k-300402" style="font-weight:bold;" target="_blank" title="Click to know more about 2K">2K</a>+ 2k` <br/> `<a href="https://interviewquestions.tuteehub.com/tag/therefore-706901" style="font-weight:bold;" target="_blank" title="Click to know more about THEREFORE">THEREFORE</a> k_(2)= <a href="https://interviewquestions.tuteehub.com/tag/4k-318773" style="font-weight:bold;" target="_blank" title="Click to know more about 4K">4K</a>` <br/> Now, `(T_2)/(T_1)= sqrt((k_1)/(k_2))= sqrt((k)/(4k))= (1)/(2)` <br/> `therefore T_(2)= (T_1)/(2)`. <br/> <img src="https://doubtnut-static.s.llnwi.net/static/physics_images/KPK_AIO_PHY_XI_P2_C14_E05_045_S01.png" width="80%"/></body></html>