Question

Disc of mass m is connected to two springs k1 and k2 as shown find time period of oscillation​

Answer 1

Time period of oscillation​ of disc mass m is connected to two springs.

Explanation:

1. Time period of spring pendulum

  $T=2\pi \sqrt{\frac{m}{k_{eff}}}$    ...1)

  where

  m = mass of oscillating object

  $k_{eff}$ = effective spring stiffness of spring system

2. Here spring system has two spring which stiffness is  $k_{1}$ and  $k_{2}$

3. If spring system is in parallel then

    $k_{eff}=k_{1}+k_{2}$     ...2)

   Now time period from equation 1) and equation 2)

    $T=2\pi \sqrt{\frac{m}{k_{eff}}} = 2\pi \sqrt{\frac{m}{k_{1}+k_{2}}}$    ...3)

4. If spring system is in series then

    $k_{eff}=\frac{k_{1}\times k_{2}}{k_{1}+k_{2}}$     ...4)

    Now time period from equation 1) and equation 4)

 $T=2\pi \sqrt{\frac{m}{k_{eff}}} = 2\pi \sqrt{\frac{m\times (k_{1}+k_{2})}{k_{1}k_{2}}}$       ...5)