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Pendulum
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Pendulum. θ rad = x/L. θ. Restoring force: F = -mg sin θ. 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 = 2 П √(m/k) = 2 П √(m/(mg/L)). T = 2 П √(L/g).
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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
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