Two blocks 1 and 2, each having mass m, are placed on a smooth table connected to three identical springs as shown in the figure. Each spring has a force constant K. Initially, all springs are relaxed. The system is disturbed and starts moving. Letx_(1) " and " x_(2) represent the displacements of the two blocks from their respective mean positions. (a) Prove that the quantity A = x_(1) + x_(2) varies sinusoidally and calculate its angularfrequency wa. (b) Prove that the quantity B = x_(1) - x_(2) varies sinusoidally and calculate its angular frequency wb. (c) Prove that motion of block 1 is superposition of two SHMs. Write frequency of the component SHMs.

Two blocks 1 and 2, each having mass m, are placed on a smooth table c

1.	Two blocks 1 and 2, each having mass m, are placed on a smooth table connected to three identical springs as shown in the figure. Each spring has a force constant K. Initially, all springs are relaxed. The system is disturbed and starts moving. Letx_(1) " and " x_(2) represent the displacements of the two blocks from their respective mean positions. (a) Prove that the quantity A = x_(1) + x_(2) varies sinusoidally and calculate its angularfrequency wa. (b) Prove that the quantity B = x_(1) - x_(2) varies sinusoidally and calculate its angular frequency wb. (c) Prove that motion of block 1 is superposition of two SHMs. Write frequency of the component SHMs.
Answer» Answer :(a) ` omega_(a)=SQRT((K)/(m))` (b)` omega_(b)=sqrt((3K)/(m))` `(c ) omega_(a) " and " omega_(b)`