Question

prove that y= a sin wt+ b cos wt represent the simple harmonic motion. Find amplitude and initial phase of SHM​

Answer 1

We have to prove that y = a sinωt + b cosωt represent the simple harmonic motion. also find Amplitude and initial phase of SHM.

proof : y = a sinωt + b cosωt

⇒y = √(a² + b²)[ a/√(a² + b²) sinωt + b/√(a² + b²) cosωt ]

let a/√(a² + b²) = cosα then b/√(a² + b²) = sinα

⇒y = √(a² + b²)[ cosα sinωt + sinα cosωt ]

= √(a² + b²) sin(ωt + α) it is also representing equation of simple harmonic motion.

hence y = a sinωt + b cosωt represents simple harmonic motion.

amplitude of y = √(a² + b²)

and initial phase = α

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The motion of a particle is given by y = 9(cm) sin(ωt) + 3(cm) cos(ωt) The motion is

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Answer 2

Answer:

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