A mass is suspended separately by two different springs in successive order then time periods is t1 and t2 respectively. If it is connected by both spring as shown in figure then time period is t0, the correct relation is

Question

A mass is suspended separately by two different springs in successive order then time periods is t1 and t2 respectively. If it is connected by both spring as shown in figure then time period is t0, the correct relation is (A)  t02 = t12 + t22  (B)  t0 - 2 = t1 -2 + t2-2  (C)  t0 - 1 = t1 - 1 + t2 - 1  (D)  t0 = t1 + t2

Tardigrade Admin · Accepted Answer

∵ T =2 π √( m / K ) ⇒ K propto (1/ T 2) In this case K = K 1+ K 2 (1/ t 02)=(1/ t 12)+(1/ t 22) ⇒ t 0-2= t 1-2+ t 2-2

Q. A mass is suspended separately by two different springs in successive order then time periods is $t_{1}$ and $t_{2}$ respectively. If it is connected by both spring as shown in figure then time period is $t_{0}$ , the correct relation is

$t_{0}^{2} = t_{1}^{2} + t_{2}^{2}$

$t_{0}^{- 2} = t_{1}^{- 2} + t_{2}^{- 2}$

$t_{0}^{- 1} = t_{1}^{- 1} + t_{2}^{- 1}$

$t_{0} = t_{1} + t_{2}$

$∵ T = 2 π \frac{m}{K}$
$\Rightarrow K \propto \frac{1}{T ^{2}}$
In this case $K = K_{1} + K_{2}$
$\frac{1}{t _{0}^{2}} = \frac{1}{t _{1}^{2}} + \frac{1}{t _{2}^{2}}$
$\Rightarrow t_{0}^{- 2} = t_{1}^{- 2} + t_{2}^{- 2}$

Q. A mass is suspended separately by two different springs in successive order then time periods is t1​ and t2​ respectively. If it is connected by both spring as shown in figure then time period is t0​, the correct relation is

t02​=t12​+t22​

t0−2​=t1−2​+t2−2​

t0−1​=t1−1​+t2−1​

t0​=t1​+t2​