Oscillations Part 1

Time period of Fig. 1 can be given as
Ta=2π√‌

M

k

where, M is mass of the suspended object and k is the force constant.
In Fig. 2, both the springs are in series combination, therefore its time period can be given as
Now, ‌

Tb

Ta

=‌

2π√ M k/2

2π√‌ M k

⇒‌‌‌

Tb

Ta

=√2...(i)
According to question, the ratio of time period of oscillation of two SHM is Tb/Ta=√x, so on comparing it with Eq. (i) we can say, x=2