Question

Several springs are connected as illustrated below in (a). Knowing the individual springs stiffness k1 = 20 N/m, k2 = 30 N/m, k3 = 15 N/m, k4 = 20 N/m, and k5 = 35 N/m, calculate the equivalent stiffness keq of this spring ensemble as in (b).

Answer 1

The equivalent stiffness of the string is 8.93 N/m.

Step-by-step explanation:

Given that,

Spring stiffness is

`k_(1)=20\ N/m`

`k_(2)=30\ N/m`

`k_(3)=15\ N/m`

`k_(4)=20\ N/m`

`k_(5)=35\ N/m`

According to figure,

`k_(2)` and
`k_(3)` is in series

We need to calculate the equivalent

Using formula for series

`(1)/(k)=(1)/(k_(2))+(1)/(k_(3))`

`k=(k_(2)k_(3))/(k_(2)+k_(3))`

Put the value into the formula

`k=(30*15)/(30+15)`

`k=10\ N/m`

k and
`k_(4)` is in parallel

We need to calculate the k'

Using formula for parallel

`k'=k+k_(4)`

Put the value into the formula

`k'=10+20`

`k'=30\ N/m`

`k_(1)`,k' and
`k_(5)` is in series

We need to calculate the equivalent stiffness of the spring

Using formula for series

`k_(eq)=(1)/(k_(1))+(1)/(k')+(1)/(k_(5))`

Put the value into the formula

`k_(eq)=(1)/(20)+(1)/(30)+(1)/(35)`

`k_(eq)=8.93\ N/m`

Hence, The equivalent stiffness of the string is 8.93 N/m.