Ch 14 covers oscillatory motion — simple harmonic motion (SHM), its mathematical description, energy analysis, the simple pendulum, and damped/forced oscillations with resonance.
SHM: restoring force proportional to displacement (F = −kx). Solution: x = A sin(ωt + φ). Velocity v = Aω cos(ωt + φ); v_max = Aω at mean position. Acceleration a = −ω²x; a_max = ω²A at extreme. Period T = 2π/ω. Spring-mass: T = 2π√(m/k). Simple pendulum: T = 2π√(l/g).
KE = ½mω²(A²−x²), PE = ½mω²x². Total E = ½mω²A² = constant. At mean position: all KE. At extreme: all PE. Damped oscillation: amplitude decreases over time due to friction (A → Ae^(−bt/2m)). Forced oscillation: external periodic force maintains amplitude. Resonance: when driving frequency equals natural frequency → maximum amplitude.
Download: https://ncert.nic.in/textbook/pdf/keph206.pdf | Part II: https://ncert.nic.in/textbook/pdf/keph2ps.zip
If soldiers march in step (rhythmically), the frequency of their footsteps might match the natural frequency of the bridge. This would cause resonance — the bridge oscillations would build up to dangerously large amplitudes, potentially causing structural failure. Breaking step ensures no single frequency drives the bridge into resonance.
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