Comparative Vibration Analysis of  a Parametrically 
                        Nonlinear Excited Oscillator  Using HPM and 
                        Numerical Method

<table>The result of HPM and RK at <svg height="9.875" id="M43" style="vertical-align:-2.29482pt" version="1.1" viewbox="0 0 10.5375 9.875" width="10.5375" xmlns="http://www.w3.org/2000/svg">
<g transform="matrix(1.25,0,0,-1.25,0,9.875)">
<g transform="translate(72,-64.1)">
<text transform="matrix(1,0,0,-1,-71.95,66.44)">
<tspan style="font-size: 12.50px; " x="0" y="0">𝜑</tspan>
</text>
</g>
</g>
</svg> = 2, <i>ε</i> = 0.01, <svg height="13.45" id="M44" style="vertical-align:-2.21957pt" version="1.1" viewbox="0 0 65.862503 13.45" width="65.862503" xmlns="http://www.w3.org/2000/svg">
<g transform="matrix(1.25,0,0,-1.25,0,13.45)">
<g transform="translate(72,-61.24)">
<text transform="matrix(1,0,0,-1,-71.95,63.5)">
<tspan style="font-size: 12.50px; " x="0" y="0">𝑥</tspan>
<tspan style="font-size: 12.50px; " x="6.8766499" y="0">(</tspan>
<tspan style="font-size: 12.50px; " x="11.040149" y="0">0</tspan>
<tspan style="font-size: 12.50px; " x="17.291649" y="0">)</tspan>
<tspan style="font-size: 12.50px; " x="24.91848" y="0">=</tspan>
<tspan style="font-size: 12.50px; " x="36.958866" y="0">0</tspan>
<tspan style="font-size: 12.50px; " x="43.210369" y="0">.</tspan>
<tspan style="font-size: 12.50px; " x="46.336117" y="0">1</tspan>
</text>
</g>
</g>
</svg>, <svg height="13.45" id="M45" style="vertical-align:-2.21957pt" version="1.1" viewbox="0 0 54.150002 13.45" width="54.150002" xmlns="http://www.w3.org/2000/svg">
<g transform="matrix(1.25,0,0,-1.25,0,13.45)">
<g transform="translate(72,-61.24)">
<text transform="matrix(1,0,0,-1,-65.27,63.5)">
<tspan style="font-size: 12.50px; " x="0" y="0">̇</tspan>
<tspan style="font-size: 12.50px; " x="-6.6766019" y="0">𝑥</tspan>
<tspan style="font-size: 12.50px; " x="0.200048" y="0">(</tspan>
<tspan style="font-size: 12.50px; " x="4.3635468" y="0">0</tspan>
<tspan style="font-size: 12.50px; " x="10.615047" y="0">)</tspan>
<tspan style="font-size: 12.50px; " x="18.241877" y="0">=</tspan>
<tspan style="font-size: 12.50px; " x="30.282267" y="0">0</tspan>
</text>
</g>
</g>
</svg>.
(a) Time history diagram of <svg height="7.1624999" id="M46" style="vertical-align:-0.11285pt" version="1.1" viewbox="0 0 8.7250004 7.1624999" width="8.7250004" xmlns="http://www.w3.org/2000/svg">
<g transform="matrix(1.25,0,0,-1.25,0,7.1625)">
<g transform="translate(72,-66.27)">
<text transform="matrix(1,0,0,-1,-71.95,66.44)">
<tspan style="font-size: 12.50px; " x="0" y="0">𝑥</tspan>
</text>
</g>
</g>
</svg>. (b) Time history diagram of <svg height="10.0125" id="M47" style="vertical-align:-0.13794pt" version="1.1" viewbox="0 0 12.625 10.0125" width="12.625" xmlns="http://www.w3.org/2000/svg">
<g transform="matrix(1.25,0,0,-1.25,0,10.0125)">
<g transform="translate(72,-63.99)">
<text transform="matrix(1,0,0,-1,-65.27,64.17)">
<tspan style="font-size: 12.50px; " x="0" y="0">̇</tspan>
<tspan style="font-size: 12.50px; " x="-6.6766019" y="0">𝑥</tspan>
<tspan style="font-size: 12.50px; " x="0.200048" y="0">.</tspan>
</text>
</g>
</g>
</svg></table>

Mathematical Problems in Engineering

fig1

Figure 1

Figure 1: Comparative Vibration Analysis of  a Parametrically 
                        Nonlinear Excited Oscillator  Using HPM and 
                        Numerical Method 

Figure 1 | Comparative Vibration Analysis of  a Parametrically 
                        Nonlinear Excited Oscillator  Using HPM and 
                        Numerical Method 

Mathematical Problems in Engineering

Comparative Vibration Analysis of a Parametrically Nonlinear Excited Oscillator Using HPM and Numerical Method

Figure 1