Two springs are joined and attached to a mass of 16 kg. The system is then suspended vertically from a rigid support. The spring constant of the two springs are k1 and k2 respectively. The period of vertical oscillations of the system will be

Question

Two springs are joined and attached to a mass of 16 kg. The system is then suspended vertically from a rigid support. The spring constant of the two springs are k1 and k2 respectively. The period of vertical oscillations of the system will be (A)  (1/8π )√k1+k2  (B)  8π √(k1+k2/k1k2)  (C)  (π /2)√k1-k2  (D)  (π /2)√(k1/k2)

Tardigrade Admin · Accepted Answer

The two springs are in series. Therefore, the time period is T=2 π √(m/k)=2 π √m((k1+k2/k1 k2)) As m=16 kg ; T=8 π √(k1+k2/k1 k2)

Q. Two springs are joined and attached to a mass of $16 k g$ . The system is then suspended vertically from a rigid support. The spring constant of the two springs are $k_{1}$ and $k_{2}$ respectively. The period of vertical oscillations of the system will be

$\frac{1}{8 π} k_{1} + k_{2}$

$8 π \frac{k _{1} + k _{2}}{k _{1} k _{2}}$

$\frac{π}{2} k_{1} - k_{2}$

$\frac{π}{2} \frac{k _{1}}{k _{2}}$

The two springs are in series. Therefore, the time period is
$T = 2 π \frac{m}{k} = 2 π m (\frac{k _{1} + k _{2}}{k _{1} k _{2}})$
As $m = 16 k g; T = 8 π \frac{k _{1} + k _{2}}{k _{1} k _{2}}$

Q. Two springs are joined and attached to a mass of 16kg. The system is then suspended vertically from a rigid support. The spring constant of the two springs are k1​ and k2​ respectively. The period of vertical oscillations of the system will be

8π1​k1​+k2​​

8πk1​k2​k1​+k2​​​

2π​k1​−k2​​

2π​k2​k1​​​