Calculation of x(t) for pendulum; differential equation and independence of mass.

Dependence of T on L, g for pendulum; m, k for spring explained qualitatively.

Demonstration that period is independent of both mass and angle θ.

Calculation of θ_max by work-energy; phase angle and oscillation equation obtained.

Angular velocity and θ calculated for uniform rod swinging on a pin; proof of simple harmonic oscillation using torque.

Explicit calculation of T for rod on a pin; demonstration to verify.

Calculation of simple harmonic oscillation and period for swinging hoop; proof that it is the same as pendulum; demonstration of period.

Period of physical pendulum calculated for arbitrary geometry.

Period of a physical pendulum, for rod, hoop, disc, and bob; experiment to verify T for rod.

To obtain the same period, dimensions of physical pendula are compared and tested.

Simple pendulum; physical pendulum, with example; center of oscillation; torsional pendulum; percussion; damped oscillations; and critical damping.

Simple pendulum; physical pendulum, with example; center of oscillation; torsional pendulum; percussion; damped oscillations; and critical damping.

Simple and physical pendulums defined, with equations for period; parallel axis theorem defined; kinetic energy of rotational motion; summary of linear and rotational dynamics.

Physical pendulum experiment setup and procedure.

Elastic and inelastic collisions between a pendulum bob and an object.

Solution (PDF)^#

Motion of a simple pendulum.

Solution (PDF)

Measuring the speed of a bullet by shooting a block suspended by two cables.

Solution (PDF)^#

Oscillation of a ruler suspended from one end.

Solution (PDF)^#

Analysis of data collected in Experiment 8.

Solution (PDF)

3-part pendulum problem; speed and kinetic energy at bottom, for two different masses.

Solution (PDF)

Motion of a baseball thrown on a small moon of Saturn.

Solution (PDF)

For inelastic collision, finding initial and final velocities and pendulum attributes.

Solution (PDF)^#

Motion of an oscillating physical pendulum.

Solution (PDF)

Period of a physical pendulum.

Solution (PDF - 1.1 MB)

Finding the period of a pendulum in a moving elevator.

Solution (PDF)

Calculating θ_max for pendulum after an inelastic collision between a bullet and a pendulum.

Solution (PDF)

5-part rotational dynamics problem; finding τ, I, equation of motion, T, and force at pin.

Solution (PDF)