Part I What is the length of a pendulum whose period is 1 second? Part II What i

Question

Part I
What is the length of a pendulum whose period is 1 second?

Part II
What is the spring constant of a spring that stretches 2.00cm when a mass of 0.600kg is suspended from it?

Part III
A simple pendulum consists of a 0.25 kg spherical mass attached to a mass-less string. When the mass is displaced slightly from its equilibrium position and released, the pendulum swings back and forth with a frequency of 2.0 Hz. What frequency would have resulted if a 0.50kg mass (same diameter) had been attached to the string instead?

Explanation / Answer

(I) Pendulum equation T = 2(L/g)1/2   ; solve for L:

L = (T/2)2g = (1 s/2)2(9.81 m/s2) = 0.2485 m

(II) F = kx so k = F/x = mg/x = (0.6 kg)(9.81 m/s2)/(0.02 m) = 294.3 N/m

(III) The same frequency, 2 Hz. See the pendulum formula in part I; period depends on the length and local gravity, but not at all on mass, and not on displacement as long as the displacement is small. This is why pendulums are useful timekeepers.

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