Four massless springs whose force constants are $$2k$$,$$2k$$, k and $$2k$$ respectively are attached to a mass M kept on a frictionless plane (as$$ shown in $$figure). If the mass M is displaced in the horizontal direction, then the frequency of oscillation of the system is

Question

Infinity Learn · Accepted Answer

The two springs on left side having spring constant of $$2k$$ each are in series, equivalent constant is $$1(12k+12k)$$ $$=$$ k. The two springs on right hand side of mass M are in parallel. Their effective spring constant is (k$$ $$+$$ $$2k) $$=$$ $$3k$$.Equivalent spring constants of value k and $$3k$$ are in parallel and their net value of spring constant of all the four springs is k $$+$$ $$3k$$ $$=$$ $$4k$$∴   Frequency of mass is n $$=$$ $$12$$$$π$$$$4kM$$

Four massless springs whose force constants are 2k,2k, k and 2k respectively are attached to a mass M kept on a frictionless plane (as shown in figure). If the mass M is displaced in the horizontal direction, then the frequency of oscillation of the system is

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