We provide sufficient conditions for the existence of periodic solutions for an idealized electrostatic actuator modeled by the Liénard-type equation <math xmlns="http://www.w3.org/1998/Math/MathML" id="M1"> <mover accent="true"> <mi>x</mi> <mo>¨</mo> </mover> <mo>+</mo> <msub> <mrow> <mi>F</mi> </mrow> <mrow> <mi>D</mi> </mrow> </msub> <mfenced open="(" close=")"> <mrow> <mi>x</mi> <mo>,</mo> <mover accent="true"> <mi>x</mi> <mo>̇</mo> </mover> </mrow> </mfenced> <mo>+</mo> <mi>x</mi> <mo>=</mo> <mi>β</mi> <msup> <mrow> <mi mathvariant="script">V</mi> </mrow> <mrow> <mn>2</mn> </mrow> </msup> <mfenced open="(" close=")"> <mrow> <mi>t</mi> </mrow> </mfenced> <mo>/</mo> <msup> <mrow> <mfenced open="(" close=")"> <mrow> <mn>1</mn> <mo>−</mo> <mi>x</mi> </mrow> </mfenced> </mrow> <mrow> <mn>2</mn> </mrow> </msup> <mo>,</mo> <mi>x</mi> <mo>∈</mo> <mfenced open="]" close="["> <mrow> <mo>−</mo> <mrow> <mo>∞</mo> </mrow> <mrow> <mo>,</mo> </mrow> <mn>1</mn> </mrow> </mfenced> </math> with <math xmlns="http://www.w3.org/1998/Math/MathML" id="M2"> <mi>β</mi> <mo>∈</mo> <msup> <mrow> <mi>ℝ</mi> </mrow> <mrow> <mo>+</mo> </mrow> </msup> </math> , <math xmlns="http://www.w3.org/1998/Math/MathML" id="M3"> <mi mathvariant="script">V</mi> <mo>∈</mo> <mi>C</mi> <mfenced open="(" close=")"> <mrow> <mi>ℝ</mi> <mo>/</mo> <mi>T</mi> <mi>ℤ</mi> </mrow> </mfenced> </math> , and <math xmlns="http://www.w3.org/1998/Math/MathML" id="M4"> <msub> <mrow> <mi>F</mi> </mrow> <mrow> <mi>D</mi> </mrow> </msub> <mfenced open="(" close=")"> <mrow> <mi>x</mi> <mo>,</mo> <mover accent="true"> <mi>x</mi> <mo>̇</mo> </mover> </mrow> </mfenced> <mo>=</mo> <mi>κ</mi> <mover accent="true"> <mi>x</mi> <mo>̇</mo> </mover> <mo>/</mo> <msup> <mrow> <mfenced open="(" close=")"> <mrow> <mn>1</mn> <mo>−</mo> <mi>x</mi> </mrow> </mfenced> </mrow> <mrow> <mn>3</mn> </mrow> </msup> </math> , <math xmlns="http://www.w3.org/1998/Math/MathML" id="M5"> <mi>κ</mi> <mo>∈</mo> <msup> <mrow> <mi>ℝ</mi> </mrow> <mrow> <mo>+</mo> </mrow> </msup> </math> (called squeeze film damping force), or <math xmlns="http://www.w3.org/1998/Math/MathML" id="M6"> <msub> <mrow> <mi>F</mi> </mrow> <mrow> <mi>D</mi> </mrow> </msub> <mfenced open="(" close=")"> <mrow> <mi>x</mi> <mo>,</mo> <mover accent="true"> <mi>x</mi> <mo>̇</mo> </mover> </mrow> </mfenced> <mo>=</mo> <mi>c</mi> <mover accent="true"> <mi>x</mi> <mo>̇</mo> </mover> </math> , <math xmlns="http://www.w3.org/1998/Math/MathML" id="M7"> <mi>c</mi> <mo>∈</mo> <msup> <mrow> <mi>ℝ</mi> </mrow> <mrow> <mo>+</mo> </mrow> </msup> </math> (called linear damping force). If <math xmlns="http://www.w3.org/1998/Math/MathML" id="M8"> <msub> <mrow> <mi>F</mi> </mrow> <mrow> <mi>D</mi> </mrow> </msub> </math> is of squeeze film type, we have proven that there exists at least two positive periodic solutions, one of them locally asymptotically stable. Meanwhile, if <math xmlns="http://www.w3.org/1998/Math/MathML" id="M9"> <msub> <mrow> <mi>F</mi> </mrow> <mrow> <mi>D</mi> </mrow> </msub> </math> is a linear damping force, we have proven that there are only two positive periodic solutions. One is unstable, and the other is locally exponentially asymptotically stable with rate of decay of <math xmlns="http://www.w3.org/1998/Math/MathML" id="M10"> <mi>c</mi> <mo>/</mo> <mn>2</mn> </math> . Our technique can be applied to a class of Liénard equations that model several microelectromechanical system devices, including the comb-drive finger model and torsional actuators.