The time period of system shown below is

Question

The time period of system shown below is (A) 2 π √(m/3 k) (B) 2 π √(2 m/k) (C) 2 π √(m/4 k) (D) 2 π √(m/k)

Tardigrade Admin · Accepted Answer

Since, the three springs with spring constants

k, k

and

2 k

are attached to the mass

m

in parallel. So, net spring constant

= k + k + 2 k = 4 k

∴

The net restoring force on mass

m

,

∣ F_{net} ∣ = - 4 k x

As, force in SHM,

∣ F_{S H M} ∣ = - m ω^{2} x

On comparing Eqs. (i) and (ii), we get

m ω^{2} = 4 k

ω = \frac{4 k}{m}

T = \frac{2 π}{ω} = 2 π \frac{m}{4 k}

Q. The time period of system shown below is