Question

The kinetic energy of a particle, executing SHM is 16 J, when it is in its mean position. If the amplitude of oscillation is 25 cm and the mass of the particle is 5.12 kg, the time period of its oscillation is ____________.

पर्याय

• `pi/5"s"`

• `2pi  "s"`

• `20pi  "s"`

• `5pi  "s"`

Answer 1

The kinetic energy of a particle, executing SHM is 16 J, when it is in its mean position. If the amplitude of oscillation is 25 cm and the mass of the particle is 5.12 kg, the time period of its oscillation is `pi/5"s"`.

Explanation:

`"K.E. at mean position" = "(K.E)"_"max"`

`= "T.E" = 1/2 "m"omega^2 "A"^2 Rightarrow1/ 2 "m"omega^2"A"^2 = 16`

`= omega^2 = (16 xx 2)/(5.12 xx 625 xx 10^-4)= 100 rightarrow omega = 10`

`therefore (2pi)/"T" = 10 Rightarrow "T" = pi/5 "s" `