A tray of mass 12 kg is supported by two identical springs as shown in figure. When the tray is pressed down slightly and released, it executes SHM with a time period of 1.5s. What is the force constant of each spring?When a block of mass m is placed on the tray , the period of SHM changes to 3.0s. What is the mass of the block ?

Explanation

Let `k_(1)` be the force constant of each spring. The total force constant of the system,
As, `T_(1)2pisqrt((m^('))/(K)) or K=(4pi^(2)m^('))/(T_(1)^(2))`
`=(4xx(22//7)^(2)xx12)/((1.5)^(2))=210.72Nm^(-1)`
`:. k_(1)=(K)/(2)=(210.72)/(2)=105.36Nm^(-1)`
Total mass, `M=m+m^(')=m+12`
`T_(2)=2pisqrt((m+m^('))/(T_(K))) or K=(4pi^(2)(m+m^(')))/(T_(2)^(2))`
`:. (4pi^(2)m^('))/(T_(1)^(2))=(4pi^(2)(m+m^(')))/(T_(2)^(2))`
or `m=(T_(2)^(2))/(T_(1)^(2))m^(')-m^(')=(3^(2))/((1.5)^(2))xx12-12`
`=48-12=36kg`