A particle executing a simple harmonic motion has a period of 6 sec. The time taken by the particle to move from the mean position to half the amplitude, starting from the mean position is.

Question

A particle executing a simple harmonic motion has a period of 6 sec. The time taken by the particle to move from the mean position to half the amplitude, starting from the mean position is. (A)  (3/2)sec (B)  (1/2)sec (C)  (3/4)sec (D)  (1/4)sec

Tardigrade Admin · Accepted Answer

Equation for simple harmonic motion y =a sin ((2 π/T)) t (a/2) =a sin ((2 π/T)) t ⇒ (2 π/T) t =(π/6) (∵ y=(a/2)) t=(T/12)=(6/12)=(1/2) s

Q. A particle executing a simple harmonic motion has a period of $6 sec$ . The time taken by the particle to move from the mean position to half the amplitude, starting from the mean position is.

$\frac{3}{2} sec$

$\frac{1}{2} sec$

$\frac{3}{4} sec$

$\frac{1}{4} sec$

Equation for simple harmonic motion
$y = a s in (\frac{2 π}{T}) t$
$\frac{a}{2} = a s in (\frac{2 π}{T}) t$
$\Rightarrow \frac{2 π}{T} t = \frac{π}{6}$
$(∵ y = \frac{a}{2})$
$t = \frac{T}{12} = \frac{6}{12} = \frac{1}{2} s$

Q. A particle executing a simple harmonic motion has a period of 6sec. The time taken by the particle to move from the mean position to half the amplitude, starting from the mean position is.

23​sec

21​sec

43​sec

41​sec