As shown in figure a simple harmonic motion oscillator having identical four springs has time period

Question

As shown in figure a simple harmonic motion oscillator having identical four springs has time period (A) T=2 π √(m/4 k) (B) T=2 π √(m/2 k) (C) T=2 π √(m/k) (D) T=2 π √(m/8 k)

Tardigrade Admin · Accepted Answer

k1 and k2 are parallel and k3 and k4 are parallel. The two combinations are in series with each other k1+k2=2 k k3+k4=4 k (1/k eq )=(1/2 k)+(1/2 k) k eq =k T=2 π √(m/k)

Q. As shown in figure a simple harmonic motion oscillator having identical four springs has time period

$T = 2 π \frac{m}{4 k}$

$T = 2 π \frac{m}{2 k}$

$T = 2 π \frac{m}{k}$

$T = 2 π \frac{m}{8 k}$

$k_{1}$ and $k_{2}$ are parallel and $k_{3}$ and $k_{4}$ are parallel. The two combinations are in series with each other
$k_{1} + k_{2} = 2 k$
$k_{3} + k_{4} = 4 k$
$\frac{1}{k _{e q}} = \frac{1}{2 k} + \frac{1}{2 k}$
$k_{e q} = k$
$T = 2 π \frac{m}{k}$

Q. As shown in figure a simple harmonic motion oscillator having identical four springs has time period

T=2π4km​​

T=2π2km​​

T=2πkm​​

T=2π8km​​

k1​ and k2​ are parallel and k3​ and k4​ are parallel. The two combinations are in series with each other k1​+k2​=2k k3​+k4​=4k keq​1​=2k1​+2k1​ keq​=k T=2πkm​​

$T = 2 π \frac{m}{4 k}$

$T = 2 π \frac{m}{2 k}$

$T = 2 π \frac{m}{k}$

$T = 2 π \frac{m}{8 k}$

$k_{1}$ and $k_{2}$ are parallel and $k_{3}$ and $k_{4}$ are parallel. The two combinations are in series with each other
$k_{1} + k_{2} = 2 k$
$k_{3} + k_{4} = 4 k$
$\frac{1}{k _{e q}} = \frac{1}{2 k} + \frac{1}{2 k}$
$k_{e q} = k$
$T = 2 π \frac{m}{k}$