The resultant spring constant of the system of springs shown below

Question

The resultant spring constant of the system of springs shown below (A) ((k1+k2)/k1+k2+k3) (B) ((4k1+2k2)(k3)/k1+k2+k3) (C) (k1+k2/2(k1+k2+k3)) (D) (k1k2k3/k1+k2+k3)

Tardigrade Admin · Accepted Answer

The first two springs are in paralleI, so their equivalent spring constant

k^{'} = k_{1} + k_{2}

Now, this combination is in series with the third spring, so their equivaient spring constant

k = \frac{k ^{'} \times k _{3}}{k ^{'} + k _{3}}

= \frac{( k _{1} + k _{2} ) ( k _{3} )}{k _{1} + k _{2} + k _{3}}

Q. The resultant spring constant of the system of springs shown below

$\frac{( k _{1} + k _{2} )}{k _{1} + k _{2} + k _{3}}$

$\frac{( 4 k _{1} + 2 k _{2} ) ( k _{3} )}{k _{1} + k _{2} + k _{3}}$

$\frac{k _{1} + k _{2}}{2 ( k _{1} + k _{2} + k _{3} )}$

$\frac{k _{1} k _{2} k _{3}}{k _{1} + k _{2} + k _{3}}$

$\frac{( k _{1} + k _{2} ) ( k _{3} )}{k _{1} + k _{2} + k _{3}}$

Q. The resultant spring constant of the system of springs shown below

k1​+k2​+k3​(k1​+k2​)​

k1​+k2​+k3​(4k1​+2k2​)(k3​)​

2(k1​+k2​+k3​)k1​+k2​​

k1​+k2​+k3​k1​k2​k3​​

k1​+k2​+k3​(k1​+k2​)(k3​)​

The first two springs are in paralleI, so their equivalent spring constant k′=k1​+k2​ Now, this combination is in series with the third spring, so their equivaient spring constant k=k′+k3​k′×k3​​ =k1​+k2​+k3​(k1​+k2​)(k3​)​

$\frac{( k _{1} + k _{2} )}{k _{1} + k _{2} + k _{3}}$

$\frac{( 4 k _{1} + 2 k _{2} ) ( k _{3} )}{k _{1} + k _{2} + k _{3}}$

$\frac{k _{1} + k _{2}}{2 ( k _{1} + k _{2} + k _{3} )}$

$\frac{k _{1} k _{2} k _{3}}{k _{1} + k _{2} + k _{3}}$

$\frac{( k _{1} + k _{2} ) ( k _{3} )}{k _{1} + k _{2} + k _{3}}$