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This is a question from a competitive test. I am not sure how to reason this out. By the length of the string, S should have the maximum amplitude. But this would be the case only when the pendulum P hits pendulum S at the point where the mass lies (the bob itself at point S). However, P is quite short for that.

Now if it hits pendulum R, then it would hit the approximately at the bob, resulting in good application of force.

However, since pendulum S is longer, it would move easily.

So the NARROWED QUESTION:

If a bob hits another bob and if a bob hits another string with a bob attached to it, the first bob and string at the same height, what effect would it have on the energies associated with the bob which gets directly hit, and on the bob which gets displaced as a result of the rope.

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I agree with Wolfram jonny that you are wrongly assuming the pendulums collide. Instead they swing in a plane perpendicular to the plane of the paper, so they never touch - see the video in the link below.

The apparatus is called "Barton's Pendulums" and is designed to illustrate Resonance.

The oscillation of pendulum P causes a periodic driving force on the horizontal string which is supporting them all. This force has the same frequency as pendulum P and is transferred through the string to the other pendulums. When the frequency of this driving force matches the natural frequency of any of the other pendulums, there is resonance - ie maximum transfer of energy from the driving force to the pendulum.

Resonance occurs here because the push from the horizontal string is 'in phase' with the matching pendulum - working with it rather than against it. The frequency of a pendulum depends on its length (not its mass) so the pendulum with the same length as P is boosted the most.

http://physicsf45spm.blogspot.co.uk/2012/03/resonance-in-bartons-pendulum.html

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  • $\begingroup$ Yep, it's called sympathetic resonance, and can be heard in some musical instruments, like piano's when the dampers are raised. The effect is strongest when the resonant freq are the same or differ one octave. Some instruments even have "sympathetic strings" that aren't usually played directly (the sitar has 15 of these). Same effect as when something in house starts rattling due to a heavy truck idling in the street. Not to be confused with synchronization between weakly coupled oscillators, first discovered by Huygens, where f. ex two pendulum clocks on a table synch in phase or antiphase. $\endgroup$
    – Previous
    Commented Jul 13, 2016 at 15:08

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