Consider a closely coiled helical spring whose one end is fixed and the other end carries a load W=mg, as shown in Fig. 1.34. Let AA be the equilibrium position of the spring after the load is attached. If the spring is stretched upto BB and then released, the load will move up and down with simple harmonic motion.
For a closely coiled helical spring, periodic time,
![Periodic time for Closely Coiled Helical Spring Periodic time for Closely Coiled Helical Spring](data:image/png;base64,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)
and frequency of oscillation,
![Frequency of oscillation for Closely Coiled Helical Spring Frequency of oscillation for Closely Coiled Helical Spring](data:image/png;base64,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)
where
s = Stiffness of the spring, and
δ = Deflection of the spring.
If the mass of the spring (m1) is also taken into consideration, then frequency of oscillation,
![Frequency of Oscillation Frequency of Oscillation](data:image/png;base64,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)
For a closely coiled helical spring, periodic time,
and frequency of oscillation,
where
s = Stiffness of the spring, and
δ = Deflection of the spring.
If the mass of the spring (m1) is also taken into consideration, then frequency of oscillation,
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