<p>A block having mass m and charge +Q is connected to aninsulating spring having a force constant k. The block lies on africtionless, insulating, horizontal track, and the system isimmersed in a uniform electric field of magnitude E directed asshown in the figure below. The block is released from rest when thespring is unstretched (at x = 0). We wish to show that the ensuingmotion of the block is simple harmonic. <br /><br/>http://www.webassign.net/serpse8/25-p-008.gif<br/><br />(b) What kinds of potential energy exist withinthis system? (Select all that apply.)<br />kinetic energy<br />gravitational potential energy <br />elasticpotential energy <br />electrical potential energy<br/><br />c) Consider the instant the block is released fromrest to be the initial configuration of the system. The finalconfiguration is when the block momentarily comes to rest again.What is the value of x when the block comes to rest momentarily?(Use any variable or symbol stated above along with the followingas necessary: π.)<br /><br />x=<br/><br />d)What is the value of x<sub>0</sub>?(Use any variable or symbol stated above along with the followingas necessary: π.)</p>

<p>x<sub>0=</sub></p>

<p>e) Define a new coordinate system <em>x</em>'such that <em>x</em>' = <em>x</em>− <em>x</em><sub>0</sub>. Showthat <em>x</em>' satisfies a differential equation forsimple harmonic motion.</p>

<p>f) Find the period of the simple harmonic motion. (Use anyvariable or symbol stated above along with the following asnecessary: <span style="font-family:georgia;"><em>π</em></span>.)</p>

<p>T=</p>

<p>g) How does the period depend on the electric fieldmagnitude?</p>

<p>A block having mass m and charge +Q is connected to aninsulating spring having a force constant k. The block lies on africtionless, insulating, horizontal track, and the system isimmersed in a uniform electric field of magnitude E directed asshown in the figure below. The block is released from rest when thespring is unstretched (at x = 0). We wish to show that the ensuingmotion of the block is simple harmonic. <br /><br/>http://www.webassign.net/serpse8/25-p-008.gif<br/><br />(b) What kinds of potential energy exist withinthis system? (Select all that apply.)<br />kinetic energy<br />gravitational potential energy <br />elasticpotential energy <br />electrical potential energy<br/><br />c) Consider the instant the block is released fromrest to be the initial configuration of the system. The finalconfiguration is when the block momentarily comes to rest again.What is the value of x when the block comes to rest momentarily?(Use any variable or symbol stated above along with the followingas necessary: π.)<br /><br />x=<br/><br />d)What is the value of x<sub>0</sub>?(Use any variable or symbol stated above along with the followingas necessary: π.)</p>

<p>x<sub>0=</sub></p>

<p>e) Define a new coordinate system <em>x</em>'such that <em>x</em>' = <em>x</em>− <em>x</em><sub>0</sub>. Showthat <em>x</em>' satisfies a differential equation forsimple harmonic motion.</p>

<p>f) Find the period of the simple harmonic motion. (Use anyvariable or symbol stated above along with the following asnecessary: <span style="font-family:georgia;"><em>π</em></span>.)</p>

<p>T=</p>

<p>g) How does the period depend on the electric fieldmagnitude?</p>