Statement of the law, with derivation of differential equation for mass on a spring.

Sinusoidal motion of mass on a spring proven through demo and differential equation; ω and T determined.

Calculation of x(t) from initial conditions for mass on a spring.

Period of spring depends on mass but not amplitude; proven by calculation and demo.

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

Proof that dU/dx=-F using mass on a spring; statement in 3D; application to gravity.

Derivation of differential equation for SHM from conservation of energy in a spring.

Kinetic and potential energy in spring at equilibrium and at x_max, using conservation.

Definition and properties of simple harmonic motion; mass-spring systems; energy in simple harmonic motions, with examples.

Definition of Hooke's law describing restoring force applied by a spring; spring constant of a coil spring; springs in parallel and series.

Definition and properties of simple harmonic motion; mass-spring systems; energy in simple harmonic motions, with examples; table of equations for simple harmonic motion.

Definition of Hooke's law describing restoring force applied by a spring; spring constant of a coil spring; springs in parallel and series.

Modeling the motion of a block-spring system using Newton's second law and conservation of mechanical energy.

Harmonic oscillator experiment setup and procedure.

Momentum and kinetic energy of a baseball bat; simple harmonic motion of two mass-spring systems.

Period, acceleration, and amplitude of harmonic motion of mass-spring systems.

Velocity of a mass in an oscillating mass-spring system.

Concept questions about elastic and inelastic collisions between two or more bodies; some questions involve mass-spring systems.

Stretching of a spring due to hanging masses.

Solution (PDF)

Finding the spring constant of a spring; finding the radius of an object in uniform circular motion.

Solution (PDF)

Fitting data from Experiment 4.

Solution (PDF)

Oscillation of a mass on a spring.

Solution (PDF)

Motion of an oscillating mass on a spring, before and after colliding with a lump of putty.

Solution (PDF)

3-part mass on a spring problem; calculating x for all t, finding v, a, energy for turning point and equilibrium.

Solution (PDF)

Finding maximum extension, time to maximum velocity for spring extended on frictional surface.

Solution (PDF)

Maximum length of cord to protect jumper; distance to water from spring constant.

Solution (PDF)

Masses m and 3m are connected by spring; finding energy, velocity, period of oscillations.

Solution (PDF)^#

Motion of a mass oscillating on a spring.

Solution (PDF)

Finding the spring constant of a spring from the maximum height of a ball shot by the spring.

Solution (PDF)

Inelastic collision of a clay ball with a block connected to a spring.

Solution (PDF)

Motion of two masses, each connected to a different spring.

Solution (PDF)

Harmonic motion of a mass connected to a spring.

Solution (PDF)

Finding ω, T, f for nut revolving around axis on end of a rubber band.

Solution (PDF)

4-part problem; finding compression necessary to launch pen into orbit; speed and radius in orbit.

Solution (PDF)^#

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

Solution (PDF)^#

Oscillation of a cart connected to a spring on an inclined plane.

Solution (PDF)^#

Inelastic collision involving an oscillating mass attached to a spring.

Solution (PDF - 1.1 MB)

5-part problem involving Hooke's Law, friction, and conservation of energy.

Solution (PDF)