Tacoma Narrows Bridge (1940) Billah and Scanlan (1991) reported that in fact, many physics textbooks (for example Resnick et al. and Tipler et al.) wrongly explain that the cause of the failure of the Tacoma Narrows bridge was externally forced mechanical resonance. Resonance is the tendency of a system to oscillate at larger amplitudes at certain frequencies, known as the system's natural frequencies. At these frequencies, even relatively small periodic driving forces can produce large amplitude vibrations, because the system stores energy. For example, a child using a swing realizes that if the pushes are properly timed, the swing can move with a very
Problem of why there is anything at all that the question cannot have a causal explanation (as any cause must itself have a cause) or a contingent explanation (as the factors giving the contingency must pre-exist), and that if there is an answer it must be something that exists necessarily (i.e. something that just exists, rather than is caused). Gottfried Wilhelm Leibniz wrote: ""Why is there something rather than nothing? The sufficient reason [...] is found in a substance which [...] is a necessary being bearing the reason for its existence within itself."" Philosopher of physics Dean Rickles has argued that numbers and mathematics (or their underlying laws)