A particle executes simple harmonic motion between $\mathrm{x}=-\mathrm{A}$ and $\mathrm{x}=+\mathrm{A}$. If time taken by particle to go from $x=0$ to $\frac{\mathrm{A}}{2}$ is 2 s ; then time taken by particle in going from $x=\frac{A}{2}$ to $A$ is :

JEE Main · 2023 · 25 Jan 2023 · Shift 2 · Elasticity & SHM

A particle executes simple harmonic motion between

x = - A

and

x = + A

. If time taken by particle to go from

x = 0

\frac{A}{2}

is 2 s ; then time taken by particle in going from

x = \frac{A}{2}

A

is :

Answer: (D)

With the motion written as

x = A sin ω t

, the particle leaves the centre at

t = 0

. Reaching

x = A /2

needs

sin ω t_{1} = \frac{1}{2}

, so

ω t_{1} = π /6

, and this stretch of phase is covered in

2

s. Reaching the extreme

x = A

needs

ω t = π /2

. The part from

A /2

A

therefore spans a phase

π /2 - π /6 = π /3

, which is twice the phase

π /6

already taken for the first

2

s. The particle crosses from

A /2

A

2 \times 2 = 4

JEE Main · 2023 · 25 Jan 2023 · Shift 2 · Single correct option