An object of mass 0-2kg executes SHM along the x-axis with frequency of 25- - Hz- At the point x-0-04m the object has KE 0-5J and PE 4J- The amplitude of oscillation is -

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Standard XII

Physics

Wave Equation

An object of ...

Question

An object of mass $0.2 k g$ executes SHM along the x-axis with frequency of $(25 / π)$ Hz. At the point $x = 0.04 m$ the object has KE $0.5 J$ and PE $4 J$ . The amplitude of oscillation is ________ .

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Solution

Whenever any object performs SHM, the total energy remains constant.
Total energy $T E$ means $K E + P E$ .
Formula :- $T E = \frac{1}{2} m ω^{2} A^{2}$
$ω = 2 π f$
$∴ 0.9 = \frac{1}{2} \times 0.2 \times 50^{2} \times A^{2}$
$\frac{9}{50^{2}} = A^{2}$ $∴ A = \frac{3}{50} = 0.06$ $m e t r e s$

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An object of mass 0.2kg executes SHM along the x-axis with frequency of (25/π) Hz. At the point x=0.04m the object has KE 0.5J and PE 4J. The amplitude of oscillation is ________ .

Whenever any object performs SHM, the total energy remains constant.Total energy TE means KE+PE.Formula :- TE=12mω2A2 ω=2πf∴0.9=12×0.2×502×A29502=A2 ∴A=350=0.06 metres

An object of mass $0.2 k g$ executes SHM along the x-axis with frequency of $(25 / π)$ Hz. At the point $x = 0.04 m$ the object has KE $0.5 J$ and PE $4 J$ . The amplitude of oscillation is ________ .