Force Law, Springs and Energy in SHM

Name: Force Law, Springs and Energy in SHM
Author: StemPy Lab

The restoring force that grows with the displacement, and the angular frequency it gives. A mass on a horizontal or a vertical spring, and springs in series and in parallel. The kinetic, potential and total energy of an oscillator.

3 lessons, about 1 h 30 min3 simulations12 problems6 practice questionsPython in every lesson

Created by StemPy Lab

Course outline (3 lessons)

Lesson 1about 30 min
The force law for simple harmonic motion
A body moves in simple harmonic motion when the force on it points back to the middle and grows in step with the displacement: $F = -kx$ . Newton's second law then gives $\omega = \sqrt{k/m}$ and $T = 2\pi\sqrt{m/k}$ . The period does not depend on the amplitude.
1 simulation2 practice questions1 Python program4 problems
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Lesson 2about 30 min
Oscillations of a spring
A spring hung from a hook stretches by $d$ with $kd = mg$ , and the load oscillates about that new rest point with the same period, $T = 2\pi\sqrt{m/k} = 2\pi\sqrt{d/g}$ . Springs side by side add their constants. Springs end to end add the inverses. A cut spring is stiffer. Two bodies on one spring oscillate with the reduced mass.
1 simulation2 practice questions1 Python program4 problems1 Python lab
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Lesson 3about 30 min
Energy in simple harmonic motion
In simple harmonic motion the energy moves back and forth between the spring and the body. The potential energy is $\tfrac12 kx^2$ , the kinetic energy is $\tfrac12 mv^2$ , and their total stays at $\tfrac12 kA^2$ . The two are equal at $x = A/\sqrt2$ , each one repeats every half period, and each one averages to half the total.
1 simulation2 practice questions1 Python program4 problems1 Python lab1 question set1 note
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Springs and Energy in SHM: Timed Test

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← Oscillations

← Periodic Motion and Simple Harmonic Motion The Simple Pendulum, Damping and Resonance →

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Force Law, Springs and Energy in SHM

Course outline (3 lessons)

The force law for simple harmonic motion

Oscillations of a spring

Energy in simple harmonic motion

Test Your Learning

Your teacher

Discussion (0)