A particle executing SHM of amplitude 4 cm and T=4 s . The time taken by it to move from positive extreme position to half the amplitude is

Question

A particle executing SHM of amplitude 4 cm and T=4 s . The time taken by it to move from positive extreme position to half the amplitude is (A) 1 s (B) (1/3) s (C) (2/3) s (D) √(3/2) s

Tardigrade Admin · Accepted Answer

Equation of motion y=acos Ït ⇒ (a/2)=acos Ït ⇒ cos Ït=(1/3) ⇒ Ït=(π /3) ⇒ (2 π t/T)=(π /3) ⇒ t=((π /3) × t/2 π )=(4/3 × 2)=(2/3) s

Q. A particle executing SHM of amplitude $4 c m$ and $T = 4 s$ . The time taken by it to move from positive extreme position to half the amplitude is

$1 s$

$\frac{1}{3} s$

$\frac{2}{3} s$

$\frac{3}{2} s$

Equation of motion $y = a cos ω t$
$\Rightarrow \frac{a}{2} = a cos ω t$
$\Rightarrow cos ω t = \frac{1}{3}$
$\Rightarrow ω t = \frac{π}{3}$
$\Rightarrow \frac{2 π t}{T} = \frac{π}{3}$
$\Rightarrow t = \frac{\frac{π}{3} \times t}{2 π} = \frac{4}{3 \times 2} = \frac{2}{3} s$

Q. A particle executing SHM of amplitude 4cm and T=4s . The time taken by it to move from positive extreme position to half the amplitude is

1s

31​s

32​s

23​​s