An object of mass 0.2 kg executes SHM along x-axis with a frequency of (16/π) Hz. At the position, x =0.04 m the object has kinetic energy 0.5 J and potential energy 0.4 J. The amplitude of oscillation is m

Question

An object of mass 0.2 kg executes SHM along x-axis with a frequency of (16/π) Hz. At the position, x =0.04 m the object has kinetic energy 0.5 J and potential energy 0.4 J. The amplitude of oscillation is m (A)  (B)  (C)  (D)

Tardigrade Admin · Accepted Answer

TE =0.5+0.4=0.9 J TE =(1/2) m ω2 a 2 ⇒ TE =(1/2) m 4 π2 v2 a 2 ⇒ 0.9 =(1/2) × 0.2 × 4 π2((16/π))((16/π)) a 2 ⇒ a =√(9/4 × 16 × 16) =(3/32) ∴ a ≈ 0.09 m

Q. An object of mass $0.2 k g$ executes SHM along $x$ -axis with a frequency of $\frac{16}{π} Hz$ . At the position, $x = 0.04 m$ the object has kinetic energy $0.5 J$ and potential energy $0.4 J$ . The amplitude of oscillation is ______m

$TE = 0.5 + 0.4 = 0.9 J$
$TE = \frac{1}{2} m ω^{2} a^{2}$
$\Rightarrow TE = \frac{1}{2} m 4 π^{2} v^{2} a^{2}$
$\Rightarrow 0.9 = \frac{1}{2} \times 0.2 \times 4 π^{2} (\frac{16}{π}) (\frac{16}{π}) a^{2}$
$\Rightarrow a = \frac{9}{4 \times 16 \times 16}$
$= \frac{3}{32}$
$∴ a \approx 0.09 m$

Q. An object of mass 0.2kg executes SHM along x-axis with a frequency of π16​Hz. At the position, x=0.04m the object has kinetic energy 0.5J and potential energy 0.4J. The amplitude of oscillation is ______m

TE=0.5+0.4=0.9J TE=21​mω2a2 ⇒TE=21​m4π2v2a2 ⇒0.9=21​×0.2×4π2(π16​)(π16​)a2 ⇒a=4×16×169​​ =323​ ∴a≈0.09m

Q. An object of mass $0.2 k g$ executes SHM along $x$ -axis with a frequency of $\frac{16}{π} Hz$ . At the position, $x = 0.04 m$ the object has kinetic energy $0.5 J$ and potential energy $0.4 J$ . The amplitude of oscillation is ______m

$TE = 0.5 + 0.4 = 0.9 J$
$TE = \frac{1}{2} m ω^{2} a^{2}$
$\Rightarrow TE = \frac{1}{2} m 4 π^{2} v^{2} a^{2}$
$\Rightarrow 0.9 = \frac{1}{2} \times 0.2 \times 4 π^{2} (\frac{16}{π}) (\frac{16}{π}) a^{2}$
$\Rightarrow a = \frac{9}{4 \times 16 \times 16}$
$= \frac{3}{32}$
$∴ a \approx 0.09 m$