A simple pendulum makes 120 complete oscillations in 3.00 min at a location wher

Question

A simple pendulum makes 120 complete oscillations in 3.00 min at a location where g- 9.80 m/s2. Find (a) the period of the pendulum and (b) its length. 2. 3.-A particle of mass m slides without friction inside a 10 hemispherical bowl of radius R. Show that if the par- ticle starts from rest with a small displacement from equilibrium, it moves in simple harmonic motion with an angular frequency equal to that of a simple pendu- lum of length R. That is, = Vg/R 4.A physical pendulum in the form of a planar object L-moves in simple harmonic motion with a frequency of 0.450 Hz. The pendulum has a mass of 2.20 kg, and the pivot is located 0.350 m from the center of mass. Deter- mine the moment of inertia of the pendulum about the pivot point.

Explanation / Answer

4. for compound pendulum,

I d^2(theta)/dt^2 + m g l theta = 0

w^2 = m g l / I

(2 x pi f )^2 = m g l / I

(2 x pi x 0.450)^2 = 2.20 x 9.8 x 0.350 / I

I = 0.94 kg m^2

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