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A block suspended from a vertical spring is in equilibrium. Show that the extension of the spring equals the length of an equivalent simple pendulum, i.e., a pendulum having frequency same as that of the block.
Let the Extension produced in the Spring be A.
Therefore, In equilibrium position,
Force due to Gravity = Spring Force.
Now, Time Period of the Spring-mass system
Now, Time period for Simple Pendulum
Now, Frequency is equal, therefore, Time period is also equal.
∴ Equating the Time Period of both the cases,
After Cancelling the terms and applying simple mathematics,
l = A,
this means the extension in the Spring equals to the length of the time period.