Question

In a spring block system if length of the spring is reduced by 1%, then time period​

Answer 1

time period will be decreased by 0.5% .

spring force, F = Kx , where k is spring constant and x is elongation or compression of spring.

if F remains constant, K ∝ 1/x .....(1)

time period of spring- mass system is given as, T = 2π√(m/K) , T ∝ 1/√K [ mass is not changing so, it remains constant ]

from equations (1),

T ∝ √x

to find error , formula will be.....

∆T/T = 1/2 ∆x/x

⇒ % error in T = 1/2 × % error in x

given, % error in x = 1%

so, % error in T = 1/2 × 1 = 0.5%

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Answer 2

$\huge\bold\purple{Answer:-}$

spring force, F = Kx , where k is spring constant and x is elongation or compression of spring.

if F remains constant, K ∝ 1/x .....(1)

time period of spring- mass system is given as, T = 2π√(m/K) , T ∝ 1/√K [ mass is not changing so, it remains constant ]

from equations (1),

T ∝ √x

to find error , formula will be.....

∆T/T = 1/2 ∆x/x

⇒ % error in T = 1/2 × % error in x

given, % error in x = 1%

so, % error in T = 1/2 × 1 = 0.5%