Restoring force proportional to displacement gives sinusoidal motion x=A cos(ωt).
SHM satisfies x''=-ω²x with solution x=A cos(ωt+φ). Period T=2π/ω, frequency f=1/T. Energy exchanges between kinetic and potential with total ½kA². Appears in pendulums, springs and electrical LC circuits.
A pendulum with L=1 m has T≈2 s for small angles.
Simple harmonic motion is the model for small oscillations, so it underlies pendulums, springs and many acoustic and electrical resonances.
Restoring force proportional to displacement gives sinusoidal motion x=A cos(ωt).
Simple harmonic motion is the model for small oscillations, so it underlies pendulums, springs and many acoustic and electrical resonances.
A restoring force that is proportional to displacement and acts toward equilibrium, which gives a sinusoidal solution in time.
The restoring torque is then proportional to sine of the angle rather than the angle itself, so the period depends on amplitude.
Typical applications include modelling a small swing of a pendulum clock, describing the motion of a mass on a spring used as a sensor and analysing the small oscillation of a moored buoy.
Study "Residual stress" first (topic 72 of 106 in Engineering Mechanics). It covers the groundwork this topic builds on.
Restoring force proportional to displacement. Amplitude independent of frequency. Phase from initial conditions.
A pendulum with L=1 m has T≈2 s for small angles.
The next topic is "Mass-spring system", which builds directly on this one.
It is classed as Advanced in Engineering Mechanics (topic 73 of 106). It is an advanced topic. It assumes you are comfortable with the intermediate topics in Engineering Mechanics.
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