A body executing S.H.M. along a straight line has a velocity of 3 ms -1 when it is at a distance of 4 m from its mean position and 4 ms -1 when it is at a distance of 3 m from its mean position. Its angular frequency and amplitude are

Question

A body executing S.H.M. along a straight line has a velocity of 3 ms -1 when it is at a distance of 4 m from its mean position and 4 ms -1 when it is at a distance of 3 m from its mean position. Its angular frequency and amplitude are (A) 2 rad s -1 5 m (B) 1 rad s -1 10 m (C) 2 rad s -1 10 m (D) 1 rad s -1 5 m

Tardigrade Admin · Accepted Answer

v=ω √A2-x2 v1=3 m / s x1=4 m v2=4 m / s x2=3 m 3=ω √A2-42 ... (i) 4=ω √A2-32 ... (ii) iolving (i) and (ii), we get A=5 m and ω=1 rad / s

Q. A body executing S.H.M. along a straight line has a velocity of $3 m s^{- 1}$ when it is at a distance of $4 m$ from its mean position and $4 m s^{- 1}$ when it is at a distance of $3 m$ from its mean position. Its angular frequency and amplitude are

$2 r a d s^{- 1} &5 m$

$1 r a d s^{- 1} &10 m$

$2 r a d s^{- 1} &10 m$

$1 r a d s^{- 1} &5 m$

$v = ω A^{2} - x^{2}$
$v_{1} = 3 m / s x_{1} = 4 m$
$v_{2} = 4 m / s x_{2} = 3 m$
$3 = ω A^{2} - 4^{2}$ ... (i)
$4 = ω A^{2} - 3^{2}$ ... (ii)
iolving (i) and (ii), we get
$A = 5 m$ and $ω = 1 r a d / s$

Q. A body executing S.H.M. along a straight line has a velocity of 3ms−1 when it is at a distance of 4m from its mean position and 4ms−1 when it is at a distance of 3m from its mean position. Its angular frequency and amplitude are

2rads−1&5m

1rads−1&10m

2rads−1&10m

1rads−1&5m