Two identical springs of spring constant '2k' are attached to a block of mass m and to fixed support (see figure).When the mass is displaced from equilibrium position on either side, it executes simple harmonic motion. The time period of oscillations of this system is:

Question

Two identical springs of spring constant '2k' are attached to a block of mass m and to fixed support (see figure).When the mass is displaced from equilibrium position on either side, it executes simple harmonic motion. The time period of oscillations of this system is: <img class="img-fluid question-image" alt="image" src="https://cdn.tardigrade.in/img/question/physics/9337a87e2484a799b8aa1c380656caa0-.png" /> (A) 2 π √( m / k ) (B) π √( m /2 k ) (C) 2 π √( m /2 k ) (D) π √( m / k )

Tardigrade Admin · Accepted Answer

For parallel combination k eq = k 1+ k 2 k eq =4 k T =2 π √( m / k eq )

Q. Two identical springs of spring constant '2k' are attached to a block of mass $m$ and to fixed support (see figure).When the mass is displaced from equilibrium position on either side, it executes simple harmonic motion. The time period of oscillations of this system is :

$2 π \frac{m}{k}$

$π \frac{m}{2 k}$

$2 π \frac{m}{2 k}$

$π \frac{m}{k}$

For parallel combination $k_{e q} = k_{1} + k_{2}$
$k_{e q} = 4 k$
$T = 2 π \frac{m}{k _{e q}}$

Q. Two identical springs of spring constant '2k' are attached to a block of mass m and to fixed support (see figure).When the mass is displaced from equilibrium position on either side, it executes simple harmonic motion. The time period of oscillations of this system is :

2πkm​​

π2km​​

2π2km​​

πkm​​