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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Hrishant Goswami , 10 Years ago
Grade 10
