A particle moves on x-axis according to the equation x=x0 sin2 ω t , the motion is simple harmonic

Question

A particle moves on x-axis according to the equation x=x0 sin2 ω t , the motion is simple harmonic (A) with amplitude x0 (B) with amplitude 2x0 (C) with time period ((2 π /ω )) (D) with time period ((π /ω ))

Tardigrade Admin · Accepted Answer

x=x0 sin 2 ω t=(x0/2)(1- cos 2 ω t)=(x0/2)-(x0/2) cos 2 ω t Frequency ω '=2ω ⇒ (2 π /T')=2 ω ⇒ T'=((π /ω )) Amplitude = (x0/2)

Q. A particle moves on x-axis according to the equation $x = x_{0} sin^{2} ω t$ , the motion is simple harmonic

with amplitude $x_{0}$

with amplitude $2 x_{0}$

with time period $(\frac{2 π}{ω})$

with time period $(\frac{π}{ω})$

$x = x_{0} sin^{2} ω t = \frac{x _{0}}{2} (1 - cos 2 ω t) = \frac{x _{0}}{2} - \frac{x _{0}}{2} cos 2 ω t$
Frequency $ω^{'} = 2 ω$
$\Rightarrow \frac{2 π}{T ^{'}} = 2 ω$
$\Rightarrow T^{'} = (\frac{π}{ω})$
Amplitude = $\frac{x _{0}}{2}$

Q. A particle moves on x-axis according to the equation x=x0​sin2ωt , the motion is simple harmonic

with amplitude x0​

with amplitude 2x0​

with time period (ω2π​)

with time period (ωπ​)