Question

The differencial equation representing the SHM of a particle is (9×d^2Y/dt^2)+4Y=0. The time period of the particle is given by:
a)π/3 sec
b)π sec
c)2π/3 sec
d)3π sec

Answer 1

answer : option (d) 3π sec

It has given that the differential equation representing the simple harmonic motion of a particle is (9 d²y/dt² ) + 4y = 0

we have to find the time period of the particle.

here, 9 d²y/dt² +4y = 0

⇒d²y/dt² = -(4/9)y

we know, for simple harmonic motion d²y/dt² = -ω²y

so, ω² = 4/9

⇒ω = 2/3

⇒2π/T = 2/3

⇒T = 3π

therefore time period of the particle is 3π sec.

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