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Determination of the stiffness constant and effective mass of a spiral spring with the method of Simple Harmonic Motion(SHM)

Theory

Description
 If the convex lens is placed on a few drops of liquid on a plane mirror, then on squeezing the liquid into the space between the mirror and the lens, a plano-concave liquid lens is formed. The surface of this liquid lens is the same radius of a curvature. Thus, we have a combination of two lenses - one of glass and one of the other liquid, which behaves as convergent lens. If f be the focal length of the combination then we have the relation.
1F = 1f1 + 1f2 ----- (1)
Where f1 and f2 are the focal length of a convex lens and the liquid lens respectivel. Correcting for the sign of f2 which is negative, we get,
1F = 1f1 + 1f2 ----- (2)
Determining F and f1 experimentally, we can calculate f2 from relation (2). The focal length f2 of plano-concave liquid lens is also given by the relation,
1f2 = (μ-1) (1r - 1rt)
= (μ-1)(1r)
= (μ-1)r
μ = 1 + rf2----- (3)
Where μ is the refractive index of the liquid.

Finding r, the radius of curvature of the lower surface of the convex lens, the surface in contact with the liquid nd knowing f2 from reltion (2), the refractive index μ of the liquid can be found out by using relation (3).

Refractive index----|-----Material
1. 501 -----|-----C6H6
2. 461 -----|-----CCl4
3. 362 -----|-----CH3OH
4. 333 -----|-----H2O

Table & Data Collection

Table-I: Data for focal length

No of obs. Distance between pins and face of lens without liquid (h1) Thickness of lens, t(cm) Focal length of the convex lens, f1=h1+t/3 Mean, f1 Distance between pins and of top surface of lens without liquid (h2) Focal length of combination, f2=h2+t/3 Mean, F Focal length of liquid lens, f2=
F x F1
F - F1
 1                
 2                
 3                

Calculations & Results

Calculation
 µ= 1 + r / f2

R = a2 ⁄ 6h + h ⁄ 2 (cm) (10 mm = 1cm)
 Error = | µ - µ' ⁄ µ | x 100 %
 Result:
The value of µ' is __
The error of µ' is __

Discussion

Point Explanation
1 The convex lens was placed on a plane mirror, and it's focal length was first determined using pin method.
2 The image pin was adjusted untill there was no parallex between the object and image pins.
3 Distance between pins was noted as without liquid.
4 The thickness of lens was clculated, then focal length of lens was calculated.
5 Distance between the pin and the top surface of lens with liquid ws taken.
6 Three observations were done.
7 Care was taken to avoid spilling or trapping air bubbles between mirror and lens.
8 Pins were kept perfectly vertical to ensure accurate alignment.
9 μ and r was calculated along with error.
10 Errors occurued due to imperfect pin alignment or imperfect distance mesurement.