A tray of mass 12 ~kg is supported by two identical springs as shown in figure. When the tray is pressed down slightly and then released, it executes SHM with a time period of 1.5 ~s . The spring constant of each spring is

Step-by-step solution

Mass of tray, m=12 ~kg Time period, T=1.5 ~s If k be the spring constant of each spring, then k₁=k₂=k Since, springs are connected in parallel, hence aligned &k_ net =k+k & Time period, T=2 m k_ net =2 m k₁+k₂ & 1.5=2 12 k+k 1.5=2 12 2 k & 1.5=2 6 k aligned Squaring both side, we have aligned 2.25 &=4 ² 6 k k &= 4 ² 6 2.25 &=105.17 Nm ⁻¹ 105 Nm ⁻¹ aligned