http://sites.science.oregonstate.edu/portfolioswiki/ 2020-01-27T03:50:25-08:00 http://sites.science.oregonstate.edu/portfolioswiki/ http://sites.science.oregonstate.edu/portfolioswiki/lib/images/favicon.ico text/html 2012-07-05T12:48:39-08:00 http://sites.science.oregonstate.edu/portfolioswiki/courses:hw:oshw:oshwcomplexrepharmonic?rev=1341517719 Homework for Complex Numbers aibiabc Homework for Complex Representations of Harmonic Motion “” text/html 2012-07-11T09:53:47-08:00 http://sites.science.oregonstate.edu/portfolioswiki/courses:hw:oshw:oshwdriven?rev=1342025627 Homework for the damped oscillator (a) Sketch the form of \(A\left( \omega \right)\). (b) Find the exact frequency at which the amplitude \(A\left( \omega \right)\) is maximal. (c) If the damping is light ($\omega_0 \beta \ll 1$), show that the frequency of maximum response (resonance frequency) is approximately \(\omega_0\), and that it differs from \(\omega _0\) by a term of order \(\beta ^{2}\). You will need to use the approximation \[(1+z)^{p}\approx 1+pz+\frac{p\left( p-1 \right)}{2!}z… text/html 2012-08-20T13:37:51-08:00 http://sites.science.oregonstate.edu/portfolioswiki/courses:hw:oshw:oshwpediagrams?rev=1345495071 Homework for Potential Energy Diagrams \begin{enumerate}\item A particle of mass $m$ and total energy $E$ that oscillates under the influence a potential energy \[U(x)=\left\{ \begin{matrix} \infty & x<0 \\ \alpha x & x\ge 0 \\ \end{matrix} \right.\] where $α$ is a known constant. Draw a diagram of the potential and label any quantities you define in your solution. Calculate the period of motion and discuss whether the is period amplitude-independent. \item Suppose the particle oscillates… text/html 2012-05-30T20:50:25-08:00 http://sites.science.oregonstate.edu/portfolioswiki/courses:hw:oshw:oshwrealrepharmonic?rev=1338436225 Homework for Real Representations of Harmonic Motion “”“” text/html 2012-08-20T13:39:21-08:00 http://sites.science.oregonstate.edu/portfolioswiki/courses:hw:oshw:oshwtopic1?rev=1345495161 Homework for Oscillations The homework for this section is the laboratory report. text/html 2012-08-21T13:29:39-08:00 http://sites.science.oregonstate.edu/portfolioswiki/courses:hw:oshw:oshwtopic2?rev=1345580979 Homework for Oscillations Calculate the natural resonance frequency of the physical pendulum used in the lab from its physical dimensions and compare with the values you measured in the lab. What approximations did you make and how important are they? text/html 2012-08-21T11:44:06-08:00 http://sites.science.oregonstate.edu/portfolioswiki/courses:hw:oshw:oshwtopic3?rev=1345574646 Homework for Oscillations Find the Fourier series that represents a square wave with period $T$, amplitude $A$. To make the problem simpler, choose the time origin so that the function is odd, and the duty cycle is 50% (duty cycle means “the time in the high state as fraction of the period”). text/html 2012-07-11T09:40:02-08:00 http://sites.science.oregonstate.edu/portfolioswiki/courses:hw:oshw:oshwunderdamped?rev=1342024802 Homework for the damped oscillator