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

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 π rad s-1 (D) 0.5 π rad s-1

Tardigrade Admin · Accepted Answer

Key Idea In SHM, Maximum velocity v max =ω A Maximum acceleration a max =A ω2 ⇒ ω =(A ω2/A ω)=(a max /v max ) v max =0.5 ms -1 a max =1.0 ms -2 ω =(1/0.5)=(10/5)=2=2 rad s -1

Q. A particle executing $S H M$ has a maximum speed of $0.5 m s^{- 1}$ and maximum acceleration of $1.0 m s^{- 2}$ The angular frequency of oscillation is

$2 r a d s^{- 1}$

$0.5 r a d s^{- 1}$

$2 π r a d s^{- 1}$

$0.5 π r a d s^{- 1}$

Key Idea In SHM,
Maximum velocity $v_{m a x} = ω A$
Maximum acceleration $a_{m a x} = A ω^{2}$
$\Rightarrow ω = \frac{A ω ^{2}}{A ω} = \frac{a _{m a x}}{v _{m a x}}$
$v_{m a x} = 0.5 m s^{- 1}$
$a_{m a x} = 1.0 m s^{- 2}$
$ω = \frac{1}{0.5} = \frac{10}{5} = 2 = 2 r a d s^{- 1}$

Q. A particle executing SHM has a maximum speed of 0.5ms−1 and maximum acceleration of 1.0ms−2 The angular frequency of oscillation is

2rads−1

0.5rads−1

2πrads−1

0.5πrads−1