The displacement y of a particle, if given by y=4cos^2⁡t/2sin⁡1000 t. This expression may be considered to be a result of the superposition of how…

Question

The displacement y of a particle, if given by y=4cos^2⁡t/2sin⁡1000 t. This expression may be considered to be a result of the superposition of how many simple harmonic motions?

MARKS Content Team · Accepted Answer

Correct answer: (B) 3. ∵ Equation of displacement of particle is y=4cos^2⁡t/2sin⁡1000t .....(i) Or y=4(1+cost)/2sin1000t ∵ cos^2⁡x=(1+cos⁡2x)/2 Or y=2sin⁡1000t+2costsin1000t Or y=2 sin1000t+sin1001t+sint 999t 2sin⁡AcosB=sin⁡A+B+sin⁡A-B Hence, equation (i) is the result of the superposition of three simple harmonic motion.

The displacement $y$ of a particle, if given by $y = 4 \cos^{2} (\frac{t}{2}) \sin (1000 t) .$ This expression may be considered to be a result of the superposition of how many simple harmonic motions?

Solution

More Oscillations Questions

The displacement y of a particle, if given by y=4cos2⁡t2sin⁡1000 t. This expression may be considered to be a result of the superposition of how many simple harmonic motions?

Solution

More Oscillations Questions

The displacement $y$ of a particle, if given by $y = 4 \cos^{2} (\frac{t}{2}) \sin (1000 t) .$ This expression may be considered to be a result of the superposition of how many simple harmonic motions?