Three SHMs act simultaneously along the same line, each with amplitude a and the same period. The second is 30° ahead of the first and the third is 30° ahead of the second. Find the resultant amplitude.
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Question

Three SHMs act simultaneously along the same line, each with amplitude a and the same period. The second is 30° ahead of the first and the third is 30° ahead of the second. Find the resultant amplitude.

Options

G1 Physics · Accepted Answer

Add three equal phasors at phases 0°,30°,60°. Resultant squared amplitude is a²[3+2(cos30°+cos30°+cos60°)]=a²[3+2(√3+1/2)]=a²(4+2√3). Therefore R=a√(4+2√3). Correct option: 1.