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Pendulum

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## Pendulum

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**Restoring force: F = -mg sinθ**If θ is small, sin θ ≈ θ F = -mg θ = -mg x/L F = -(mg/L) x F = -kx Force constant (k) = mg/L**For small angles, pendulum is SHM**period: T = 2П √(m/k) = 2 П √(m/(mg/L)) T = 2 П √(L/g) f = (1/ 2 П) √(g/L)**k**If the mass on the spring and the pendulum have the same period, what is the length of the pendulum? m1g/k**Energy of a Pendulum**θ L PEmax? vmax?**k**v M Arrow sticks into block. Maximum compression of spring?