Two identical leaf spring of spring constant k are arranged like cantilever in parallel and attached at free end by a spring of spring constant k,. The equivalent spring constant of combination is?

Question

Answer

Calculation of Equivalent Spring Constant in Parallel Arrangement

Explanation

When two identical leaf springs of spring constant k are arranged in parallel, the equivalent spring constant of the combination can be calculated as follows:

Step 1: Calculation of Individual Spring Constant

Each leaf spring has a spring constant k. Therefore, the spring constant of each leaf spring is k.

Step 2: Calculation of Equivalent Spring Constant of Two Leaf Springs in Parallel

When two leaf springs are arranged in parallel, their equivalent spring constant is given by the formula:

1/keq = 1/k + 1/k

Simplifying the above equation, we get:

keq = 2k

Therefore, the equivalent spring constant of two leaf springs arranged in parallel is 2k.

Step 3: Calculation of Equivalent Spring Constant of the Combination

The two leaf springs arranged in parallel are attached at their free ends by a spring of spring constant k. Therefore, the equivalent spring constant of the combination is given by the formula:

1/keq = 1/(2k) + 1/k

Simplifying the above equation, we get:

keq = 4/3 k

Therefore, the equivalent spring constant of the combination is 4/3 k.

Conclusion

When two identical leaf springs of spring constant k are arranged in parallel and attached at their free ends by a spring of spring constant k, the equivalent spring constant of the combination is 4/3 k.

Answer

Answer

Parallel

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