Two particles A and B perform SHM along the same straight line with the same amplitude a, frequency f and equilibrium position O. The greatest distance between them is 3a/2. At some instant they have the same displacement from the mean position. What is the displacement?
Options

Question

Two particles A and B perform SHM along the same straight line with the same amplitude a, frequency f and equilibrium position O. The greatest distance between them is 3a/2. At some instant they have the same displacement from the mean position. What is the displacement?

Options

G1 Physics · Accepted Answer

For equal-amplitude SHMs with phase difference δ, maximum separation is 2a sin(δ/2). Given 2a sin(δ/2)=3a/2, so sin(δ/2)=3/4. At an instant when their displacements are equal, the common magnitude is a cos(δ/2)=a√[1−(3/4)²]=a√7/4. Correct option: 2.