All the springs in fig (a), (b) and (c) are identical, each one having force constant K. Mass m is attached to each system. If $T_{a}$ , $T_{b}$ and $T_{c}$ are the periodic time of oscillations of the three systems in fig (a), (b) and (c) respectively, then

Question

TestHub · Accepted Answer

For figure (a), the equivalent spring constant is $K_{a} = K$ .

The time period of oscillation is $T_{a} = 2 π \frac{m}{K}$ .

For figure (b), the two springs are connected in series. The equivalent spring constant is $K_{b} = \frac{K \cdot K}{K + K} = \frac{K}{2}$ .

The time period is $T_{b} = 2 π \frac{m}{K /2} = 2 π \frac{2 m}{K} = 2 (2 π \frac{m}{K}) = 2 T_{a}$ .

For figure (c), the two springs are connected in parallel. The equivalent spring constant is $K_{c} = K + K = 2 K$ .

The time period is $T_{c} = 2 π \frac{m}{2 K} = \frac{1}{2} (2 π \frac{m}{K}) = \frac{T _{a}}{2}$ .

From the expression for $T_{c}$ , we can write $T_{a} = 2 T_{c}$ .

Substituting this value of $T_{a}$ into the expression for $T_{b}$ :

$T_{b} = 2 (2 T_{c}) = 2 T_{c}$ .

Physics - SHM Question with Solution | TestHub

Options:

Doubts & Discussion