# Mass on a Spring

## Hooke's Law

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

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

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Stretching of a spring due to hanging masses.

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## Sinusoidal Motion

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

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## Mass on a Spring Example

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

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• Watch {}video clip from Lecture 10 (16:51 - 20:29)

## Hooke's Law Demonstration

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

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• Watch {}video clip from Lecture 10 (20:29 - 29:07)

## Spring and Pendulum Comparison

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

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• Watch {}video clip from Lecture 10 (36:22 - 40:49)

## Force and Potential Energy

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

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• Watch {}video clip from Lecture 13 (7:00 - 14:56)

## Simple Harmonic Motion from Energy Conservation

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

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• Watch {}video clip from Lecture 13 (19:35 - 24:43)

## Energy in a Spring

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

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## Oscillatory Motion

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

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

## Mechanical Energy Problem Solving

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

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## Experiment 6

Harmonic oscillator experiment setup and procedure.

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## Simple Harmonic Motion

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

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## Mass-Spring Oscillation

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

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## Oscillating Mass-Spring

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

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## Collisions

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

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## Experiment 4 Pre-Lab

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

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## Experiment 4 Analysis

Fitting data from Experiment 4.

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## Spring-Mass Harmonic Oscillator

Oscillation of a mass on a spring.

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## Inelastic Collision with an Oscillating Mass

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

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## Mass on a Spring

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

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Motion of a mass oscillating on a spring.

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

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## Spring with Friction

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

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## Bungee Jumping

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

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## Distinct Masses Connected by Spring

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

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## Spring-Launched Ball

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

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## Collision with Mass on a Spring

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

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## Spring Compression

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

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## Oscillating Mass on a Spring

Harmonic motion of a mass connected to a spring.

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## Experimental Centripetal Force

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

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## Marooned on an Asteroid

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

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## Inelastic Collision with a Spring

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

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## Block and Spring

Inelastic collision involving an oscillating mass attached to a spring.

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## Spring on an Inclined Plane

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

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