- #1
hidemi
- 208
- 36
- Homework Statement
- The angular frequency of a simple pendulum depends on its length and on the local acceleration due to gravity. The rate at which the angular displacement of the pendulum changes, dθ/dt, is:
A. √ (mgL/I)
B. √(g/L)
C. 2兀 (L/g)
D. √(k/m)
E. none of the above
- Relevant Equations
- F=-kx
T=2兀/w
w = √(g/L)
I think the answer should be B, not E.
Here's the reasoning:
F = -kx = mg sinθ = -mg θ (because θ very small) = -mgx/L
T = 2π*√(m/k) = 2π*√(m/(mg/L)) = 2π*√(L/g)
Also, T= 2π/w and thus, w = dθ/dt = √(g/L)
Here's the reasoning:
F = -kx = mg sinθ = -mg θ (because θ very small) = -mgx/L
T = 2π*√(m/k) = 2π*√(m/(mg/L)) = 2π*√(L/g)
Also, T= 2π/w and thus, w = dθ/dt = √(g/L)