Question

A particle is executing S.H.M. with amplitude of 4 cm and time period 12 s. The time taken by the particle in going from its mean position to a position of displacement equal to 2 cm is T₁ The time taken from this displaced position of 2 cm to reach the extreme position is T₂. T₁/ T₂ will be____________.

पर्याय

• 2

• 1

• `1/2`

• `1/3`

Answer 1

A particle is executing S.H.M. with amplitude of 4 cm and time period 12 s. The time taken by the particle in going from its mean position to a position of displacement equal to 2 cm is T₁ The time taken from this displaced position of 2 cm to reach the extreme position is T₂. T₁/ T₂ will be `1/2`.

Explanation:

`"y" = 4sin  (2pi)/12t`

Now,y₁ = 2cm

`therefore 2 = 4"sin"  pi/6t or 1/2 = "sin"  pi/6t_1`

`therefore pi/6t_1 = pi/6 or "t"_1 = 1"s"`

`therefore "T"_1 = "t"_1 - 0 = 1"s"`

Again, y₂ = 4 cm

`therefore 4 = 4sin  pi/6"t"_2  or pi/6"t"_2 = pi/2 or "t"_2 = 3"s"`

T₂ = t₂ - t₁ = 3 - 1 = 2 s

`therefore "T"_1 : "T"_2 = 1 : 2`