Infinite oscillating springs

Classical Mechanics Level 3

There is a system of infinite pulleys and springs as shown in the figure above. Spring constants follows a geometric progression, K , 2 K , 4 K , 8 K , … K, 2K, 4K, 8K, \ldots . All the pulleys are massless and frictionless. Find the time period of oscillation.

Take the mass of the block to be m m . If the answer is of the form T = 2 π B m / K T =2\pi \sqrt{Bm/K} , where B B is a natural number, submit your answer as B B .


The answer is 8.

Nitin Sachan by Nitin Sachan , 37, India

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1 solution

Md Zuhair
Jan 9, 2018

Can this be the solution....

We have.... By constraint equation

x = 2 x 1 + 2 x 2 + 2 x 3 + . . . ∞ x=2x_{1}+2x_{2}+2x_{3}+...\infty

T k e q = 4 T k + 4 T 2 k + . . . ∞ \dfrac{T}{k_{eq}}=\dfrac{4T}{k}+\dfrac{4T}{2k}+...\infty

⟹ 1 k e q = 8 k \implies \dfrac{1}{k{eq}}=\dfrac{8}{k}

So T = 2 π 8 k m T=2 \pi \sqrt{\dfrac{8k}{m}}

2 Helpful 0 Interesting 0 Brilliant 1 Confused

Don't understand. Pls explain

Apoorva Singal - 4 months, 3 weeks ago

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