{"product_id":"wilberforces-spring-plate-005-physics-poster","title":"Wilberforce's Spring – Plate 005 Physics Poster","description":"\u003cp\u003ePlate 5 speaks for itself: \u003cem\u003e“Bob, then twist, then bob again.”\u003c\/em\u003e\u003c\/p\u003e\u003ch3\u003eThe Physics\u003c\/h3\u003e\u003cp\u003eA mass on a helical spring can bob up and down and twist. The spring weakly couples the two motions, so when their frequencies are tuned equal the energy swaps slowly between bobbing and twisting, like two coupled pendulums beating.\u003c\/p\u003e\u003cp\u003e\u003cstrong\u003ef_T = (1\/2π)√(k\/m) ≈ f_R = (1\/2π)√(κ\/I)\u003c\/strong\u003e\u003c\/p\u003e\u003cul\u003e\n\u003cli\u003ef_T, f_R: translational and rotational frequencies, Hz\u003c\/li\u003e\n\u003cli\u003ek: spring constant, N m⁻¹\u003c\/li\u003e\n\u003cli\u003em: bob mass, kg\u003c\/li\u003e\n\u003cli\u003eκ: torsion constant, N m rad⁻¹\u003c\/li\u003e\n\u003cli\u003eI: bob moment of inertia about the spring axis, kg m²\u003c\/li\u003e\n\u003c\/ul\u003e\u003cp\u003eTuned so f_T ≈ f_R, the energy swaps from bobbing to twisting and back. Wilberforce, 1894.\u003c\/p\u003e\u003ch3\u003eSources\u003c\/h3\u003e\u003cul\u003e\n\u003cli\u003eL. R. Wilberforce, Phil. Mag. 38, 386 (1894).\u003c\/li\u003e\n\u003cli\u003eR. E. Berg, T. S. Marshall, Am. J. Phys. 59, 32 (1991).\u003c\/li\u003e\n\u003c\/ul\u003e\u003ch3\u003eOn the poster\u003c\/h3\u003e\u003cp\u003ePlate 005, “Wilberforce's Spring”: the pixel-art plate with its slogan “Bob, then twist, then bob again.”, the key equation and the facts panel shown above. Pixelated Physics. Physics. Personified.\u003c\/p\u003e","brand":"Printify","offers":[{"title":"9'' x 12\" (Vertical) \/ Matte","offer_id":50961480286311,"sku":"57269859059692846975","price":19.99,"currency_code":"USD","in_stock":true},{"title":"9'' x 12\" (Vertical) \/ Fine Art","offer_id":50961480319079,"sku":"33178813353036160402","price":29.99,"currency_code":"USD","in_stock":true},{"title":"9'' x 12\" (Vertical) \/ Semi Glossy","offer_id":50961480351847,"sku":"31870145457060662476","price":19.99,"currency_code":"USD","in_stock":true},{"title":"18″ x 24″ (Vertical) \/ Fine Art","offer_id":50961480384615,"sku":"18999377442760405301","price":44.99,"currency_code":"USD","in_stock":true},{"title":"18″ x 24″ (Vertical) \/ Semi Glossy","offer_id":50961480417383,"sku":"89976685108993661740","price":29.99,"currency_code":"USD","in_stock":true},{"title":"18″ x 24″ (Vertical) \/ Matte","offer_id":50961480450151,"sku":"69464215612509594296","price":29.99,"currency_code":"USD","in_stock":true},{"title":"36'' x 48\" (Vertical) \/ Matte","offer_id":50961480482919,"sku":"25384968502505155238","price":69.99,"currency_code":"USD","in_stock":true},{"title":"36'' x 48\" (Vertical) \/ Fine Art","offer_id":50961480515687,"sku":"11630097189415585630","price":119.99,"currency_code":"USD","in_stock":true},{"title":"36'' x 48\" (Vertical) \/ Semi Glossy","offer_id":50961480548455,"sku":"26475951108403026646","price":69.99,"currency_code":"USD","in_stock":true}],"thumbnail_url":"\/\/cdn.shopify.com\/s\/files\/1\/0596\/8746\/9159\/files\/1886330842557946114_2048.jpg?v=1793730248","url":"https:\/\/pixelatedphysics.com\/it\/products\/wilberforces-spring-plate-005-physics-poster","provider":"Pixelated Physics","version":"1.0","type":"link"}