Question

A particle executing $SHM$ has a maximum speed of $0.5 \, ms^{ -1}$ and maximum acceleration of $1.0 \, ms^{-2}$ The angular frequency of oscillation is

• A. $2 \, rad \, s^{-1}$
• B. $0.5 \, rad \, s^{-1}$
• C. $2\,\pi \, rad \, s^{-1}$
• D. $0.5\, \pi \, rad \, s^{-1}$

Answer 1

Answer: (A)

Key Idea In SHM,
Maximum velocity $v_{\max }=\omega A$
Maximum acceleration $a_{\max }=A \omega^{2}$
$\Rightarrow \omega =\frac{A \omega^{2}}{A \omega}=\frac{a_{\max }}{v_{\max }}$
$v_{\max } =0.5 \,ms ^{-1}$
$a_{\max } =1.0 \,ms ^{-2}$
$\omega =\frac{1}{0.5}=\frac{10}{5}=2=2\, rad s ^{-1}$