תנועה הרמונית פשוטה

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F = −k·x   |   ω = √km   |   T = 2πω   |   f = 1T
40 N/m
0.25 kg
0.20 m
0.00
0.00
0.00
0.00
0.00
0.00
0.00

F = −k·x ω = √km
ω = √km = √400.25 = √160 = 12.65 rad/s
T = 2πω = 6.28312.65 = 0.497 s
f = 1T = 10.497 = 2.01 Hz


x(t) = A·cos(ωt + φ)   |   v(t) = −Aω·sin(ωt + φ)   |   a(t) = −Aω²·cos(ωt + φ) = −ω²·x
T = 2πω   |   f = 1T   |   ω = 2πT
0.20 m
4.0 rad/s
0°
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0.000
0.00
0.00
0°
0.00
0.00
0.000

T = 2πω = 6.2836.0 = 1.047 s f = 1T = 11.047 s = 0.955 Hz
v(t) = −Aω·sin(ωt)    vmax = Aω = 0.08 · 6.0 = 0.48 m/s
a(t) = −Aω²·cos(ωt)    amax = Aω² = 0.08 · 36 = 2.88 m/s²
ωt + φ = 6.0 · 0.25 + 0 = 1.5 rad = 1.5 · 180°π = 85.9° x = 0.08 · cos(1.5 rad) = 0.08 · 0.0707 = 0.0057 m

Δx₀ = mgk   |   T = 2π√mk   |   ΣF = −k·y
20 N/m
0.50 kg
10 cm
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0.00
0.0
0.0
0.00
0.00
0.00
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0.00

k · Δx₀ = mg = 0.50 · 9.8 = 4.9 N
Δx₀ = mgk = 0.50 · 9.820 = 4.920 = 0.245 m = 24.5 cm
T = 2π√mk = 2π√0.5020 = 2π · 0.1581 = 0.99 s f = 1T = 10.9935 = 1.01 Hz
ΣF = mg − k(Δx₀ + y) = mg − k · mgk − k·y = −k·y

Fמחזיר = −mg·sinθ  ≈  −mg·θ   |   T = 2π√Lg
1.00 m
1.0 kg
15°
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0
0
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T = 2π√Lg
T = 2π√1.09.8 = 2π · 0.3194 = 2.01 s
T² = 4π²·Lg  ⟹  L = g·T²4π² = 9.8 · 1.0²39.478 = 0.248 m
m·L·θ̈ = −m·g·sinθ  ⟹  θ̈ = −gL·sinθ
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