A block of mass m is connected to three springs as shown in the figure. The block is displaced down slightly and left free, it starts oscillating. Find the time period of oscillations (neglecting gravity). (m=π2 kg ; π2=10 ; θ=60° ; k1=4 N / m ; k2=23 N / m )

Question

A block of mass m is connected to three springs as shown in the figure. The block is displaced down slightly and left free, it starts oscillating. Find the time period of oscillations (neglecting gravity). (m=π2 kg ; π2=10 ; θ=60° ; k1=4 N / m ; k2=23 N / m ) (A)  (B)  (C)  (D)

Tardigrade Admin · Accepted Answer

<img class="img-fluid question-image" alt="image" src="https://cdn.tardigrade.in/img/question/physics/497944a903a7b16a404903d9929e6044-.png" /> at GP F text restoring =2 k1 x cos 2 θ +k2 x So, T=2 π √(m/2 k1 cos 2 θ +k2)

Q. A block of mass $m$ is connected to three springs as shown in the figure. The block is displaced down slightly and left free, it starts oscillating. Find the time period of oscillations (neglecting gravity).
$(m = π^{2} k g; π^{2} = 10; θ = 6 0^{\circ}; k_{1} = 4 N / m; k_{2} = 23 N / m)$

at $GP$
$F_{restoring} = 2 k_{1} x cos^{2} θ + k_{2} x$
So, $T = 2 π \frac{m}{2 k _{1} c o s ^{2} θ + k _{2}}$

Q. A block of mass m is connected to three springs as shown in the figure. The block is displaced down slightly and left free, it starts oscillating. Find the time period of oscillations (neglecting gravity). (m=π2kg;π2=10;θ=60∘;k1​=4N/m;k2​=23N/m)

at GP Frestoring ​=2k1​xcos2θ+k2​x So, T=2π2k1​cos2θ+k2​m​​

Q. A block of mass $m$ is connected to three springs as shown in the figure. The block is displaced down slightly and left free, it starts oscillating. Find the time period of oscillations (neglecting gravity).
$(m = π^{2} k g; π^{2} = 10; θ = 6 0^{\circ}; k_{1} = 4 N / m; k_{2} = 23 N / m)$

at $GP$
$F_{restoring} = 2 k_{1} x cos^{2} θ + k_{2} x$
So, $T = 2 π \frac{m}{2 k _{1} c o s ^{2} θ + k _{2}}$