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

Question

The displacement y of a particle, if given by y=4 cos 2(t / 2) sin (1000 t). This expression may be considered to be a result of the superposition of how many simple harmonic motions? (A) 2 (B) 3 (C) 4 (D) 5

Tardigrade Admin · Accepted Answer

∵ Equation of displacement of particle is y=4 cos 2((t/2)) sin (1000 t) ...(i) or y=4[((1+ cos t/2)) sin 1000 t] (∵ cos 2 x=(1+ cos 2 x/2)) or y=3 sin 1000 t+2 cos t sin 1000 t or y=2 sin 1000 t+ sin 1001 t+ sin t 999 t [2 sin A cos B= sin (A+B)+ sin (A-B)] Hence, Eq. (i) is the result of the superposition of three simple harmonic motion.

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

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6

Q. The displacement y of a particle, if given by y=4cos2(t/2)sin(1000t). This expression may be considered to be a result of the superposition of how many simple harmonic motions?

2

3

4

5

6

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