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?

Step-by-step solution

∵ Equation of displacement of particle is y = 4 cos 2 ⁡ t 2 sin ⁡ 1000 t .....(i) Or y = 4 1 + c o s t 2 s i n 1000 t ∵ cos 2 ⁡ x = 1 + cos ⁡ 2 x 2 Or y = 2 sin ⁡ 1000 t + 2 c o s t s i n 1000 t Or y = 2 s i n 1000 t + s i n 1001 t + s i n t 999 t 2 sin ⁡ A c o s B = sin ⁡ A + B + sin ⁡ A - B Hence, equation (i) is the result of the superposition of three simple harmonic motion.