A particle executes simple harmonic motion under the restoring force provided by a spring. The time period is T. If the spring is divided in two equal parts and' one part is used to continue the simple harmonic motion, the time period will

Question

A particle executes simple harmonic motion under the restoring force provided by a spring. The time period is T. If the spring is divided in two equal parts and' one part is used to continue the simple harmonic motion, the time period will (A) remain T (B) become 2 T (C) become T / 2 (D) none of these

Tardigrade Admin · Accepted Answer

(1/k')+(1/k')=(1/k) ⇒ k'=2 k T=2 π √(m/k) and T'=2 π √(m/2 k) (T'/T)=(1/√2) or T'=(T/√2)

Q. A particle executes simple harmonic motion under the restoring force provided by a spring. The time period is $T$ . If the spring is divided in two equal parts and' one part is used to continue the simple harmonic motion, the time period will

remain $T$

become $2 T$

become $T /2$

none of these

$\frac{1}{k ^{'}} + \frac{1}{k ^{'}} = \frac{1}{k}$
$\Rightarrow k^{'} = 2 k$
$T = 2 π \frac{m}{k}$ and $T^{'} = 2 π \frac{m}{2 k}$
$\frac{T ^{'}}{T} = \frac{1}{2}$ or $T^{'} = \frac{T}{2}$

Q. A particle executes simple harmonic motion under the restoring force provided by a spring. The time period is T. If the spring is divided in two equal parts and' one part is used to continue the simple harmonic motion, the time period will

remain T

become 2T

become T/2