As shown in the figure, a block of mass m is connected to two unstretched springs having spring constants k₁ and k₂ . The block is displaced towards the right by a distance x and subsequently released. Determine the speed of the block when it passes through the indicated mean position.

Step-by-step solution

When the block is displaced by a distance x towards the right, the left spring is stretched by x and the right spring is compressed by x . Both springs exert a restoring force in the same direction (towards the left). The total restoring force on the block is: F = -k₁ x - k₂ x = -(k₁ + k₂)x This shows that the two springs act as a parallel combination with an equivalent spring constant: k_ eq = k₁ + k₂ The potential energy stored in the system at the extreme position is: U = 1 2 k_ eq x^2 = 1 2 (k₁ + k₂) x^2 When t