In the figure, a block of mass M = 490 g placed on a frictionless table is connected with two springs having same spring constant K = 2 N m⁻¹. If the block is displaced horizontally, the number of complete oscillations it will make in 14π s is ______. Image
Physics · Circular Motion
JEE Mains 31 January 2023 Shift 1 Morning Shift

Question

In the figure, a block of mass M = 490 g placed on a frictionless table is connected with two springs having same spring constant K = 2 N m⁻¹. If the block is displaced horizontally, the number of complete oscillations it will make in 14π s is ______. Image

Physics · Circular Motion

JEE Mains 31 January 2023 Shift 1 Morning Shift

G1 Physics · Accepted Answer

Both springs provide restoring force, so k(eff)=2K=4 N m⁻¹. With m=0.49 kg, T=2π√(m/k)=2π√(0.49/4)=7π/10 s. Number of oscillations in 14π s is 14π/(7π/10)=20.