Time period of a spring-mass system is T . If this spring is cut into two parts whose lengths are in the ratio 1:3 and the same mass is attached to the longer part, the new time period will be

Question

Time period of a spring-mass system is T . If this spring is cut into two parts whose lengths are in the ratio 1:3 and the same mass is attached to the longer part, the new time period will be (A) √(3/2) T (B) (T/√3) (C) (√3 T/2) (D) √3T

Tardigrade Admin · Accepted Answer

T =2 π √( m / k ) When spring is cut in the ratio 1: 3, the force constant of the longer part is (4 k /3). ∴ T prime=2 π √(3 m /4 k )=(√3/2) T

Q. Time period of a spring-mass system is $T$ . If this spring is cut into two parts whose lengths are in the ratio $1 : 3$ and the same mass is attached to the longer part, the new time period will be

$\frac{3}{2} T$

$\frac{T}{3}$

$\frac{3 T}{2}$

$3 T$

$T = 2 π \frac{m}{k}$
When spring is cut in the ratio $1 : 3$ , the force constant of the longer part is $\frac{4 k}{3}$ .
$∴ T^{'} = 2 π \frac{3 m}{4 k} = \frac{3}{2} T$

Q. Time period of a spring-mass system is T . If this spring is cut into two parts whose lengths are in the ratio 1:3 and the same mass is attached to the longer part, the new time period will be

23​​T

3​T​

23​T​

3​T