A mass is suspended separately by two different springs in successive order, then time periods are t1 and t2 respectively. If it is connected by both springs as shown in figure then time period is t0, the correct relation is [figure]
- t02 = t12 + t22
- t0-2 = t1-2 + t2-2
- t0-1 = t1-1 + t2-1
- t0 = t1 + t2
Answer
(2) t0-2 = t1-2 + t2-2
Solution
For a spring–mass system: t = 2 mk k = 4 2mt2
The two springs in the figure are in parallel: k0 = k1 + k2
4 2mt02 = 4 2mt12 + 4 2mt22
t0-2 = t1-2 + t2-2
Answer: (2)