Is the Elastic String Pulley System REALLY a HARD Problem in IIT JEE Physics?

IIT JEE and other engineering entrance examinations has been asking questions from mechanics and SHM with mass, spring and pulley combination for long period of time in consistent manner. Some times there are more than one problem from this area. Therefore, it is very important for students to get the concepts and practice right.

Here is the problem description

Two particles of mass m are attached to the ends of an inextensible string which hangs over a smooth pulley. To one of the particles A another particle B of mass 2m is attached by means of an elastic string of natural length a and spring constant k. If the system is supported with elastic string just un-stretched and then released, find the acceleration with which A descends.


Steps to solve the problem.

1. Understand logically what's going on, what could be the motion once it is set to move
2. Draw free body diagram, choose axes strategically
3. Write F=ma for all the masses
4. Solve for d2x/st2 and d2y/dt2
5. Come up with SHM equation, compute frequency of oscillation
6. Compute the acceleration for block A

Introduction: 0:06
Problem Statement: 1:05
FBD: 3:42
F=ma: 6:15
d2y/dt2: 9:40
SHM equation: 11:35
d2x/dt2: 14:58

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