.What is spring factor? Derive the expression for resultant spring constant when two springs having force constants 1 k and 2 k are connected in (i) parallel and (ii) in series
Answers
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
respectively. A constant force
is exerted on the rod so that remains perpendicular to the direction of the force. So that the springs are extended by the same amount. Alternatively, the direction of force could be reversed so that the springs are compressed
This system of two parallel springs is equivalent to a single Hookean spring, of spring constant
can be found from the formula that applies to capacitors connected in parallel in an electrical circuit.
When same springs are connected as shown in the figure below, these are said to be connected in series. A constant force
is applied on spring 2. So that the springs are extended and the total extension of the combination is the sum of elongation of each spring. Alternatively, the direction of force could be reversed so that the springs are compressed.