This above article throw light on the spring constant experiment of VTU.

1. Experiment No.: 03
DETERMINATION OF SPRING CONSTANT
AIM: a) To determine spring constant for the material of the given springs and
b) To determine Spring constant in series and parallel combination.
APPARATUS: Given springs, slotted weights, meter scale, pointer etc.
PRINCIPLE: The springs are the elastic material working on the principle of Hook’s law. The
expansion or compression of the springs takes place by the application of stress along the of axis
of the spring and also the extension and compression is dependent on the direction in which force
applied. Whensubjected to stress, the restoring force is always directed opposite to displacement.
Therefore, Restoring force α – displacement
F = - k x
Here “k” is the proportionality constant known as spring constant. It is a relative measure of
stiffness of the material.
Springs in Series:
When two springs with spring constants k1 and k2 respectively are connected in series and a
mass m suspended at the end, the force ‘F’ acting on both springs, also effective force is F.
Spring 1 expands by length ‘x1’, F = - k1x1,  x1 = - F/k1 ,
Spring 2 expands by length ‘x2’, F = - k2x2,  x2 = - F/k2
Total expansion is given by ‘x’ F = - kx,  x= - F/k
Also, x = x1 + x2
Therefore,
𝐹
𝑘
=
𝐹
𝑘1
+
𝐹
𝑘2
Solving above equation we get
1
𝑘
=
1
𝑘1
+
1
𝑘2
Effective spring constant when connected in series is
𝒌 =
𝒌𝟏 + 𝒌𝟐
𝒌𝟏 × 𝒌𝟐
Springs in Parallel:
When two springs constant k1 and k2 respectively are connected in parallel both springs expand with
same length ‘x’ on application of mass ‘m’ as shown in fig.

2. By the application of Hooks law we have
For spring 1, F1= - k1x ---------------1
For spring 2 F2 = -k2x -----------------2
The effective force on combination is given by
F = -kx --------------------------------------3
Also F = F1 +F2 ------------------------ 4
Substitute the values from equations equations 1,2,3 in 4.
-kx = - (k1x + k2x)  kx = k1x + k2x
Which gives k = k1+k2
Therefore effective spring constant of two springs connected in parallel is given by sum of constant of
two springs.
PROCEDURE:
1. Connect the given spring to a rigid support.
2. Attach the weight hanger (dead load) to the end of the spring and note down the initial
displacement “a” produced on the scale.
3. Increase the weight in steps of 50 g and note down the displacement (b) produced in the
spring. Find the elongation (b-a) . Using the formula (1) find spring constant K1.
4. Repeat the above steps and find spring constant K2 for the second spring.
5. Connect the two springs in series combination and repeat the above procedure to find kseries.
6. Connect the two springs in parallel combination and repeat the above procedure to find kparallel.
7. Compare the experimental results obtained with the theoretical value.
Diagrams:

3. Tabular column:
Determination of spring constant for spring 1:
Value of initiation load (W) = __________________ kg
Displacement for the initial load a =___________ m.
Trial
no
Mass M
(kg )
F = Mg
(N)
Displacement
b
(m)
Elongation
∆X= (b-a)
(m)
Spring
constant K1
(N/m)
1 W+ 0.05
2 W+0.1
3 W+0.15
4 W+0.2
Average K1= ...........................N/m
Determination of spring constant for spring 2
Value of initiation load (W) = __________________ kg
Displacement for the initial load a =___________ m.
Trial no Mass M
(kg )
F = Mg
(N)
Displacementb
(m)
Elongation
∆X= (b-a)
(m)
Spring
constant K2
(N/m)
1 W+ 0.05
2 W+0.1
3 W+0.15
4 W+0.2
Average K2=.................................................... N/m
Determination of spring constant in series combination:
Value of initiation load (W) = __________________ kg
Displacement for the initial load a =___________ m.
Trial
no
Mass M
(kg )
F =Mg
(N)
Displacement ‘b’
(m)
Elongation
∆X= (b-a)
(m)
Spring constant
Kseries
(N/m)
1 W+ 0.05
2 W+0.1
3 W+0.15
4 W+0.2
Average Kseries=......................................................... N/m

4. Calculated value of spring constant for Series combination = 𝒌 =
𝒌𝟏+𝒌𝟐
𝒌𝟏×𝒌𝟐
.
=
=___________________N/m
Determination of spring constant in parallel combination
Value of initiation load (W) = __________________ kg
Displacement for the initial load a =___________ m.
Tr. no Mass M
kg
F = Mg
(N)
Displacement
‘b’
(m)
Elongation
∆X= (b-a)
(m)
Spring
constant
Kparallel (N/m)
1 W+ 0.05
2 W+0.1
3 W+0.15
4 W+0.2
Average kparallel=..................................N/m
Calculated value of spring constant for Parallel combination= k1 +k2
=
=___________________N/m
Result:
1. The spring constant of the given material of the springs are found to be
K1= ....................N/m
K2 ................................ N/m.
2. Spring constants in series and parallel combinations are found to be
Combination Calculated (N/m) Experimental (N/m)
Series k series = k series =
Parallel k parallel = k parallel =
****