Question

the displacement equation of a particle is x = 3sin2t + 4cos2t. the amplitude and maximum velocity will be​

Answer 1

SOLUTION.

When you see such equation with cos and sine operator with equal Angle than please take a look on its coefficients Divide and multiply by roots of addition of its coefficients.

X = 3Sin(2t) + 4Cos(2t)

Multiply and divide by √3²+4² = 5

X = (3/5)Sin(2t) + (4/5)Cos(2t)

Now the value of cos∆ = 3/5

when ∆ = 53°

The value of Sin[©] = 4/5

when © = 53°

X = Cos(53°)Sin(2t) + Cos(2t)Sin53°

X = Sin( 2t + 53° )

X = A sin(wt + Φ )

By comparing We get

Amplitude = 1unit

And w = 2

MAXIMUM VELOCITY = A.w

MAXIMUM VELOCITY = 2unit/sec

#Answerwithquality

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