NEET2015PhysicsOscillationsActual
When two displacements represented by y 1 = a   s i n ⁡ ( ω t ) and y 2 = b cos ⁡ ω t are superimposed the motion is:
Options
- Anot a simple harmonic.
- Bsimple harmonic with amplitude a b .
- Csimple harmonic with amplitude a 2 + b 2 .
- Dsimple harmonic with amplitude a + b 2 .
Correct answer
C. simple harmonic with amplitude a 2 + b 2 .
Step-by-step solution
y 1 = a sin ⁡ ω t y 2 = b cos ⁡ ω t = b sin ⁡ ω t + π 2 Amplitude A = a 2 + b 2 + 2 a b cos ⁡ π 2 A = a 2 + b 2 Since the frequency for both motion are same, then the resultant motion will be SHM.