366lab7

# 366lab7 - 3 A stiff spring will oscillate faster When k = 2...

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y ' = v v ' = - 0.25 y -5 -4 -3 -2 -1 0 1 2 3 4 5 -2 -1.5 -1 -0.5 0 0.5 1 1.5 2 y v y ' = v v ' = - 0.25 y -20 -10 0 10 20 30 -3 -2 -1 0 1 2 3 t y 1. Period: about 10s I’d consider this a slow oscillation. Amplitude : about 7cm

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2. y’’+ 0.25y=0 r^2 + 0.25 = 0 r^2 = -0.25 r =-0.5i r=0.5i y = C1*cos0.5t+C2*sin0.5t y(0) = C1 = 3 y’(0) = -0.5C1*sin0.5t + 0.5C2*cos0.5t = 0.5C2 = -1 C2 = -2 y= 3cos0.5t-2sin0.5t y= √13cos(0.5t+0.188pi) amplitude : √13 = 3.6 cm period : 2pi/0.5 = 4pi = 12.56s
y ' = v v ' = - 2 y -5 -4 -3 -2 -1 0 1 2 3 4 5 -6 -4 -2 0 2 4 6 y v y ' = v v ' = - 2 y -10 0 10 20 30 40 50 -3 -2 -1 0 1 2 3 t y

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Unformatted text preview: 3. A stiff spring will oscillate faster. When k = 2, period is about 5s. Comparing with the period when k = 0.25, it oscillates faster. 4. 5. y’’ + 0.25y = 1.8sin0.5t 6. 7. In Physics, resonance is the tendency of a system to oscillate at lager amplitude at some frequencies than at others. These are known as the system’s resonant frequencies. At these frequencies, even small periodic driving forces can produce large amplitude oscillations.(WIKI)...
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366lab7 - 3 A stiff spring will oscillate faster When k = 2...

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