6.2 Problems
249
Fig. 6.8
uniform rod about one end is I =
1
3
M L 2 , obtain an equation for the period
of the oscillatory motion for small angles. What would be the length l of a
simple pendulum that has the same period as the swinging rod?
6.33 The physical pendulum has two possible pivot points A and B, distance L
apart, such that the period of oscillations is the same (Fig. 6.9). Show that
the acceleration due to gravity at the pendulum’s location is given by g =
4π 2 L/T 2 .
Fig. 6.9
6.34 A semi-circular homogeneous disc of radius R and mass m is pivoted freely
about the centre. If slightly tilted through a small angle and released, find the
angular frequency of oscillations.
6.35 A ring is suspended on a nail. It can oscillate in its plane with time period T 1
or it can oscillate back and forth in a direction perpendicular to the plane of
the ring with time period T 2 . Find the ratio T 1 /T 2 .
6.36 A torsional oscillator consists of a flat metal disc suspended by a wire. For
small angular displacements show that time period is given by
T = 2π
I
C
249
Fig. 6.8
uniform rod about one end is I =
1
3
M L 2 , obtain an equation for the period
of the oscillatory motion for small angles. What would be the length l of a
simple pendulum that has the same period as the swinging rod?
6.33 The physical pendulum has two possible pivot points A and B, distance L
apart, such that the period of oscillations is the same (Fig. 6.9). Show that
the acceleration due to gravity at the pendulum’s location is given by g =
4π 2 L/T 2 .
Fig. 6.9
6.34 A semi-circular homogeneous disc of radius R and mass m is pivoted freely
about the centre. If slightly tilted through a small angle and released, find the
angular frequency of oscillations.
6.35 A ring is suspended on a nail. It can oscillate in its plane with time period T 1
or it can oscillate back and forth in a direction perpendicular to the plane of
the ring with time period T 2 . Find the ratio T 1 /T 2 .
6.36 A torsional oscillator consists of a flat metal disc suspended by a wire. For
small angular displacements show that time period is given by
T = 2π
I
C