A 3 kg block is connected as shown in the figure. Spring constants of two springs \( K_1 \) and \( K_2 \) are 50 Nm\(^{-1}\) and 150 Nm\(^{-1}\) respectively. The block is released from rest with the springs unstretched. The acceleration of the block in its lowest position is ( \( g = 10 \) ms\(^{-2}\) )
A 4 kg mass is suspended as shown in the figure. All pulleys are frictionless and spring constant \( K \) is \( 8 \times 10^3 \) Nm\(^{-1}\). The extension in spring is ( \( g = 10 \) ms\(^{-2}\) )
The variance for continuous probability function \(f(x) = x^2 e^{-x}\) when \(x \ge 0\) is
Consider the loop transfer function \(\frac {K(s+6)}{(s+3)(s+5)}\). In the root locus diagram the centroid will be located at:
When nuclear radiations pass through, gas ionization is produced. This is the principle of which of the following detectors?
If \(f = \text{Tan}^{-1}(xy)\) then \((\frac{\partial f}{\partial x})_{(1,2)}\) = _____ .