What is the spring constant in parallel connection and series connection?
1 Answer
Parallel.
When two massless springs following Hooke's Law, are connected via a thin, vertical rod as shown in the figure below, these are said to be connected in parallel. Spring 1 and 2 have spring constants
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This system of two parallel springs is equivalent to a single Hookean spring, of spring constant
k=k_1+k_2
Series.
When same springs are connected as shown in the figure below, these are said to be connected in series. A constant force
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This system of two springs in series is equivalent to a single spring, of spring constant
For spring 1, from Hooke's Law
F=k_1x_1
where
Similarly if
F=k_2x_2
Total deformation of the system
x_1+x_2=F/k_1+F/k_2
=>x_1+x_2=F(1/k_1+1/k_2)
Rewriting and comparing with Hooke's law we get
k=(1/k_1+1/k_2)^-1