13.4 Which of the following functions of time represent

PHYSICS · Multi-part · AP · Physics 1: Algebra-based · Oscillations · Oscillations

Problem

13.4 Which of the following functions of time represent (a) simple harmonic, (b) periodic but not simple harmonic, and (c) non-periodic motion? Give period for each case of periodic motion ( ω\omega is any positive constant): (a) sin⁡ωt−cos⁡ωt\sin \omega t-\cos \omega t (b) sin⁡3ωt\sin ^{3} \omega t (c) 3cos⁡(π/4−2ωt)3 \cos (\pi / 4-2 \omega t) (d) cos⁡ωt+cos⁡3ωt+cos⁡5ωt\cos \omega t+\cos 3 \omega t+\cos 5 \omega t (e) exp⁡(−ω2t2)\exp \left(-\omega^{2} t^{2}\right) (f) 1+ωt+ω2t21+\omega t+\omega^{2} t^{2}

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