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Oscillations

A system of s...

Question

A system of springs with their spring constant are as shown in figure. The frequency of oscillations of the mass m will be (assuming the springs to be massless)

\frac{1}{2 π} \sqrt{\frac{k_{1} k_{2} (k_{3} + k_{4})}{[(k_{1} + k_{2}) + (k_{3} + k_{4}) + K_{1} K_{4}] m}}

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\frac{1}{2 π} \sqrt{\frac{k_{1} k_{2} (k_{3} + k_{4})}{[(k_{1} + k_{2}) (k_{3} + k_{4}) + K_{1} K_{2}] m}}

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\frac{1}{2 π} \sqrt{\frac{k_{1} k_{2} (k_{3} + k_{4})}{[(k_{1} + k_{2}) + (k_{3} + k_{4}) + K_{1} K_{3}] m}}

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\sqrt{\frac{(k_{1} + k_{2}) (k_{3} + k_{4})}{k_{1} k_{2} (k_{3} + k_{4}) m}}

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Solution

The correct option is A $\frac{1}{2 π} \sqrt{\frac{k_{1} k_{2} (k_{3} + k_{4})}{[(k_{1} + k_{2}) + (k_{3} + k_{4}) + K_{1} K_{4}] m}}$
$K_{n e t} = \frac{K_{1} K_{2} (K_{3} + K_{4})}{K_{1} K_{2} + K_{1} (K_{3} + K_{4}) + K_{2} (K_{3} + K_{4})} = \frac{K_{1} K_{2} (K_{3} + K_{4})}{K_{1} K_{2} + (K_{3} + K_{4}) (K_{1} + K_{2})} f = \frac{1}{2 π} \sqrt{\frac{K}{m}}$

= $\frac{1}{2 π} \sqrt{\frac{k_{1} k_{2} (k_{3} + k_{4})}{[(k_{1} + k_{2}) (k_{3} + k_{4}) + K_{1} K_{2}] m}}$

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A system of springs with their spring constant are as shown in figure. The frequency of oscillations of the mass m will be (assuming the springs to be massless)

The correct option is A 12π√k1k2(k3+k4)[(k1+k2)+(k3+k4)+K1K4]mKnet=K1K2(K3+K4)K1K2+K1(K3+K4)+K2(K3+K4)=K1K2(K3+K4)K1K2+(K3+K4)(K1+K2)f=12π√Km=12π√k1k2(k3+k4)[(k1+k2)(k3+k4)+K1K2]m