All springs and pulley are ideal. If m mass disturbed slightly from its equilibrium then its time period is 2 π d ( k 1 k 2 k 3 ) m [ a ( k 1 k 3 ) + b ( k 2 k 3 ) + c ( k 1 k 2 ) ] , where a , b , c & d are least integer value then find ( a + b + c − d ) .

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PhysicsSHMCalculation of time periodMedium3 minQB

PhysicsMediuminteger

All springs and pulley are ideal. If m mass disturbed slightly from its equilibrium then its time period is $2 π \frac{m [ a ( k _{1} k _{3} ) + b ( k _{2} k _{3} ) + c ( k _{1} k _{2} ) ]}{d ( k _{1} k _{2} k _{3} )}$ , where $a, b, c & d$ are least integer value then find $(a + b + c - d)$ .

Answer:

Solution:

Reduce the spring-pulley network to an effective stiffness acting on m, using the constraint relations of the strings.

Comparing $T = 2 π m / k_{eff}$ with the given form fixes the least integers a, b, c, d.

The combination gives $a + b + c - d = 5$ .

Answer: 5

Stream:JEESubject:PhysicsTopic:SHMSubtopic:Calculation of time period

⏱ 3mℹ️ Source: QB

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