Motions {simple harmonic motion}| can oscillate along lines, with acceleration proportional to distance from center point. Molecule-bond vibrations, springs, pendulums, rigid-bar vibrations, rotations, guitar-string vibrations, bridge vibrations, and tall-building sway have simple harmonic motion.
force
Restoring-force strength depends on material type and distance from center. For molecule bonds, spring constant depends on electrical forces between atoms. Restoring force F equals negative of spring constant k expressing restoring force strength times displacement x: F = -k*x. Restoring force is negative because it opposes displacement.
amplitude
Amplitude depends on input energy, which causes more or less displacement.
period
One oscillation takes one time period. Period depends on material restoring force. Period and amplitude are independent. Spring period T is 360 degrees expressed in radians 2*pi times square root of mass m divided by spring constant k: T = 2 * pi * (m/k)^0.5. Higher mass makes longer period. Higher spring constant makes shorter period.
energy
Potential energy PE equals half spring constant k times displacement x squared, which is average force, k*x/2, times distance x: PE = 0.5 * k * x^2. At center, force equals zero, and potential energy equals zero. At maximum displacement amplitude, force and potential energy are highest. At maximum displacement, kinetic energy equals zero, because motion stops as direction reverses. At center, velocity and kinetic energy maximize, because potential energy is zero.
velocity
Maximum velocity v is maximum displacement A times square root of spring constant k divided by object mass m: v = A * (k/m)^0.5. Average velocity is 4*A/T, where A is amplitude and T is period. Average velocity is 2 * v / pi, where v is maximum velocity.
friction
If friction damps simple harmonic motion, amplitude decreases, but frequency stays the same, because material is the same.
When pulled sideways and released, weight {pendulum} hanging by string or wire from point starts oscillating motion.
force
Pendulum restoring force is gravity. Gravity g pulls pendulum-bob mass m back toward center with force F from distance x, depending on displacement angle A: F = m * g * sin(A) = m * k * x.
distance
If pendulum displacement is small, displacement-angle sine equals displacement angle: sin(A) = A. For small displacement, displacement x is displacement angle, expressed in radians, times pendulum length L: x = A*L. For small displacement, constant k is gravity acceleration g divided by pendulum length L: k = g/L.
period
Pendulum period T is 360 degrees, expressed in radians 2*pi, times square root of gravitational-constant reciprocal 1/g: T = 2 * pi * (1/g)^0.5. Longer pendulums have longer periods. Weaker gravity makes longer period. Pendulum mass does not affect period.
Spring oscillation time T {period, oscillation}| is 360 degrees, expressed in radians 2*pi, times square root of mass m divided by spring constant k: T = 2 * pi * (m/k)^0.5. Higher mass makes longer period. Higher spring constant makes shorter period.
Springiness {spring constant, force} depends on length, cross-sectional area, and force strength between molecules. Stiff springs {spring, metal}| have high spring constant.
5-Physics-Dynamics-Force-Kinds
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Date Modified: 2022.0225