May 31st, 2015, 11:04 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 11:14 PM. Reason: no specific reason 
June 1st, 2015, 06:15 PM  #2 
Math Team Joined: Jul 2011 From: Texas Posts: 2,815 Thanks: 1458 
$\displaystyle T = 2\pi \sqrt{\frac{L}{g}}$ 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, 03:40 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 

Tags 
$$$, entrance, exam, level, mechanics, pendulum, physics, shm 
Thread Tools  
Display Modes  

Similar Threads  
Thread  Thread Starter  Forum  Replies  Last Post 
German college entrance test (need little help)  hypnotize  Algebra  5  January 20th, 2015 01:16 PM 
need help urgently have entrance exam tomorrow  jessmari86  Calculus  4  April 11th, 2011 05:55 PM 
Iranian college post graduation course entrance exams  Saeid  Math Events  6  February 27th, 2011 04:22 AM 
HOT.university entrance exam in Vietnam.HOT  dmc0929  Algebra  2  July 7th, 2009 11:06 AM 
Help for College entrance math exam  eagles24548  Algebra  5  May 10th, 2009 03:28 PM 