If the length of the spring is doubled, there will be no effect on its period.
If the mass of the spring is doubled and the spring constant is halved, then its period will be doubled.
The Simple Harmonic Motion is a type of periodic motion and one of its examples is the spring-mass system.
The period of a spring mass system is given by the following equation,
T= 2π√m/√k
Here, T= period of spring
m= Mass of the body attached to the spring
k= Spring constant
According to the above equation, the period of a spring depends on the mass of the body and the spring constant.
It is independent of the length of the spring.
Therefore, if the length of spring is doubled then there will be no effect on its period.
If the mass of spring is doubled and the spring constant is halved, then the equation becomes
T'= 2π√2m/√k/2
T'= √4 x 2π√m/√k
T'= 2 x T
Hence, if the mass of the spring is doubled and the spring constant is halved, its period will be doubled.
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