For a particle performing linear S.H.M., its average speed over one oscillation is (a = amplitude of S.H.M., n = frequency of oscillation)

Question

For a particle performing linear S.H.M., its average speed over one oscillation is (a = amplitude of S.H.M., n = frequency of oscillation) (A) 2 an (B) 4 an (C) 6 an (D) 8 an

Tardigrade Admin · Accepted Answer

Given, amplitude of SHM = a Frequency of oscillation =n Distance travelled in one oscillation, =4 × text amplitude of SHM =4 a We know that, text Velocity =( text Distance travelled in one oscillation / text Time period ) v =(4 a/T) ∴ v=4 a n [∵. Frequency, .n=(1/T)]

Q. For a particle performing linear S.H.M., its average speed over one oscillation is (a = amplitude of S.H.M., n = frequency of oscillation)

$2 an$

$4 an$

$6 an$

$8 an$

Given, amplitude of $S H M = a$
Frequency of oscillation $= n$
Distance travelled in one oscillation,
$= 4 \times amplitude of S H M = 4 a$
We know that,
$Velocity = \frac{Distance travelled in one oscillation}{Time period}$
$v = \frac{4 a}{T}$
$∴ v = 4 an$ $[∵$ Frequency, $n = \frac{1}{T}]$