Question

The maximum speed and acceleration of a particle executing simple harmonic motion are $10cm{s}^{-1}and50cm{s}^{-2}$. Find the position(s) of the particle when the speed is $8c{m}^{-1}$.

• A. $\pm 5cm$
• B. $\pm 1.2cm$
• C. $\pm 3.8cm$
• D. $\pm 4.6cm$

Answer 1

The correct option is B

$\pm 1.2cm$

Max speed

$v=A\omega =10$ ...(1)

max acceleration

$a=A{\omega }^2=50$ ...(ii)

Dividing (ii) with (i)

$\omega =5$ ...(iii)

substituting (iii) in (i)

$10=A\times 5$

$A=2$ ...(iv)
We derived the relation between v and x as.

$v=\omega \sqrt{A^2-x^2}$

To find x when v = 8

$8=5\sqrt{4-x^2}$

$x^2=4-\frac{64}{25}x=\sqrt{\frac{36}{25}}=\pm \frac{6}{5}=\pm 1.2cm$