A particle executes a simple harmonic motion of time period T . Find the time taken by the particle to go directly from its mean position to half the amplitude

Question

A particle executes a simple harmonic motion of time period T . Find the time taken by the particle to go directly from its mean position to half the amplitude (A)  T/2  (B)  T/4  (C)  T/8  (D)  T/12

Tardigrade Admin · Accepted Answer

y=a sin ω t=(a sin 2 π/T) t At the mean position y=(a/2) (a/2)=(a sin 2 π t/T) t=(T/12)

Q. A particle executes a simple harmonic motion of time period $T$ . Find the time taken by the particle to go directly from its mean position to half the amplitude

$T /2$

$T /4$

$T /8$

$T /12$

$y = a sin ω t = \frac{a s i n 2 π}{T} t$
At the mean position $y = \frac{a}{2}$
$\frac{a}{2} = \frac{a s i n 2 π t}{T}$
$t = \frac{T}{12}$

Q. A particle executes a simple harmonic motion of time period T . Find the time taken by the particle to go directly from its mean position to half the amplitude

T/2

T/4

T/8

T/12