A mass on a string traces a horizontal circle while the string makes angle theta with the vertical.

Force balance:

• Vertical: T*cos(theta) = mg
• Horizontal: Tsin(theta) = momega^2r = momega^2Lsin(theta)

Results:

• omega = sqrt(g/(L*cos(theta)))
• T (tension) = mg/cos(theta) > mg
• Period: T_p = 2pisqrt(Lcos(theta)/g) = 2pisqrt(h/g), where h = Lcos(theta)

Key insight: The period depends only on the vertical height h below the support point, not independently on L and theta. A longer string at the same angle gives a longer period (proportional to sqrt(L)).

The string can never be perfectly horizontal (theta = 90 would require infinite tension to support mg).