Periodic Time of Spring and Spring Constant – Rankers Physics
Topic: Oscillation
Subtopic: Spring Block System

Periodic Time of Spring and Spring Constant

Assertion (A): The periodic time of a hard spring is less as compared to that of a soft spring.
Reason (R): The spring constant is large for hard spring.
 
Both (A) & (R) are true and the (R) is the correct explanation of the (A)
Both (A) & (R) are true but the (R) is not the correct explanation of the (A)
(A) is true but (R) is false
Both (A) and (R) are false

Solution:

The periodic time of a spring is given by `\(T = 2\pi\sqrt{\frac{m}{k}}\)`.
A hard spring has a large spring constant `\(k\)`, which means a smaller `\(T\)`. A soft spring has a small `\(k\)`, hence a larger `\(T\)`. Both A and R are true, and R explains A.

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