Question

Consider a simple harmonic motion of time period T. Calculate the time taken for the displacement to change the value from half the amplitude to the amplitude.

Answer 1

Since, the motion is a simple Harmonic. Therefore, its equation will be given by the formula,

x = ASin(wt + Φ)

Now, for first travelling,

x = A/2

we will get,

Sin(ωt + Φ) = 1/2

Φ = 0, in initial phase.

∴ ωt = π/6

t₁ = π/6ω

For second Journey, from A/2 to A,

x = ASin(ωt + Φ)

Sin(ωt) = Sinπ/2

ωt = π/2

t₂ = π/2ω

Time taken from A/2 to A = π/2ω - π/6ω

= π/3ω

Now, ω = 2π/T

∴ Time taken = π/3(2π/T)

  =T/6.

Hope it helps.