Grade 10Wave Motion
Driven nonlinear oscillators do not need to oscillate at the driving frequency. Consider the driven quartic oscillator
where m, k, F, and ωd are constants. Show that x(t) = A cos ωt is a solution to this equation if (1) ω = ωd/3 and (2) F ∝ ![src=data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAEkAAAAhCAIAAAAathG8AAABcklEQVRYhe2X0RWDIAxFmSsDZZ5MwzIZxn4AShCRBD1Fj++r1kpz85Igbnmv3L8DuFETszGB24RevcC8bB4dEK+f3XbVq3nZhDwanHsCGxPoTVtmZ/M40G6LK3tWyJKtOzTSbwFPPGxb7i4xgd67WJM1knxQdStW0XhSRJMxgX1Oql3aCjnL5lh7lNpWMybLxFZ2aCDpXsPjnp0JLm+AOlu7HD1mzoTsou/siJAWJOba95f4vSpn6xyRTCBiWF08Dywl4nDdS8eXwbf9zd5WL6tWFMBygq6Xod9K31bXz4LahV6yNZxLxaEBt8wSEVKMB/HcuhG2+GtVxV4yJ4E4Rd5aYxd6tUYPrVHvt/l7icbw2laWDaSDlUTwKUMp4JprRRYb2JW75fvk4JhKeM1JJEPN/14+ltva3mIO2SaVpLGcc6ZlKyaH5XA6NZtw7UXn7sw3jwChIplAQTgtmzxpxAvLHvBOfWzP1Mf2Tdivsz9Sb2X4hfdL1QDHjlAAAAABJRU5ErkJggg==]()
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