Question

A body executing simple harmonic motion has a maximum acceleration equal to $24metres/ ⥂ sec^{2}$ and maximum velocity equal to$16\mspace{6mu} metres/ ⥂ \sec$. The amplitude of the simple harmonic motion is

• A. $\frac{32}{3}metres$
• B. $\frac{3}{32}metres$
• C. $\frac{1024}{9}metres$
• D. $\frac{64}{9}metres$

Answer 1

Answer: (A)

$\frac{32}{3}metres$

Answer 2

Maximum velocity $= a\omega$ = 16

Maximum acceleration $= \omega^{2}a = 24$

$\Rightarrow a = \frac{(a\omega)^{2}}{\omega^{2}a} = \frac{16 \times 16}{24} = \frac{32}{3}m$