As per given figures, two springs of spring constants K and 2 K are connected to mass m . If the period of oscillation in figure (a) is 3 s , then the period of oscillation in figure (b) will be x s . The value of x is _____ .

Step-by-step solution

In figure (a), the springs are connected in series. Therefore, K eq = K 1 K 2 K 1 + K 2 = K × 2 K K + 2 K = 2 K 3 Therefore, the time period T a = 2 π m K eq = 2 π m 2 K 3 = 2 π 3 m 2 K In figure (b), the springs are connected in parallel. Therefore, K e q = K 1 + K 2 = 3 K Therefore, the time period T b = 2 π m K eq = 2 π m 3 K Now, T a T b = 9 2 ⇒ T b = 2 3 T a = 2   s Hence, x = 2