May 31st, 2015, 10:04 PM  #1 
Newbie Joined: May 2015 From: INDIA Posts: 28 Thanks: 1  \$\$\$ entrance exam level \$\$\$
A pendulum has time period T for small oscillations. An obstacle P is situated below the point of suspension O at a distance 3L/4 (from the top). The pendulum is released from rest. Throughout the motion, the moving string makes a small angle with the vertical. Time after which the pendulum returns back to its initial position is what? The length of the pendulum is L. The correct answer is 3T/4, but why have we assumed half oscillation after the obstacle where the time period does not depend on gravity component? Explain and I will press the thanks button. Last edited by skipjack; May 31st, 2015 at 10:14 PM. Reason: no specific reason 
June 1st, 2015, 05:15 PM  #2 
Math Team Joined: Jul 2011 From: Texas Posts: 2,947 Thanks: 1555 
$\displaystyle T = 2\pi \sqrt{\frac{L}{g}}$ released from rest, the time to hit the obstacle is $\displaystyle \frac{T}{4}$ once it hits the obstacle, the new length is $\displaystyle \frac{L}{4}$ which cuts the period $T$ in half ... after hitting the obstacle, $\displaystyle \frac{T}{8}$ up, $\displaystyle \frac{T}{8}$ down ... back to original length, $\displaystyle \frac{T}{4}$ back to the start. $\displaystyle \frac{T}{4} + \frac{T}{8} + \frac{T}{8} + \frac{T}{4} = \frac{3T}{4}$ 
July 2nd, 2015, 02:40 AM  #3 
Newbie Joined: May 2015 From: INDIA Posts: 28 Thanks: 1 
will you please explain how time period gets T/8 up and down after hitting 

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