Determine the equivalent spring constant for the system show

Determine the equivalent spring constant for the system shown below.

Solution

>> For Parallel Combination of Two Springs,

Ax, Displacement is same.

So, x1 = x2 =x

As, Net Force, F = F1 + F2

=> K*x = K1*x1 + K2*x2

=> K = k1 +k2 , i.e,

Equivalent Spring Constant is Summation of all....

>> In Series System,

As, Force is same in each spring,

=> F = F1 = F2

and, x = x1 + x2 [ Because net Displacement = Sum of individual spring displacements ]

=> F/K = F1/K1 + F2/K2

=> 1/K = 1/K1 + 1/K2 , i.e,

Reciprocal of Equivalent Spring Constant is sum of reciprocalof individual spring constants

>> Now, in our system, k1 & k2 are in parallel

So Let, K\" = Equivalent of these two

=> K\" = k1 + k2

>> Now, This K\" & k3 are in Series.

Let, K = Equivalent Spring Constant of the whole system

So,

1/K = 1/K\" + 1/k3

=> K = (K\")(k3)/[K\" + k3]

=> K = (k1 + k2)*(k3)/[k1 + k2 + k3] .......ANSWER........