How do you calculate the angular FREQUENCY given the amplitude and the maximum velocity the object travels at (through the point of equilibrium)???
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An harmonic oscillator describes a position:
x(t) = A cos(ω t + φ)
Where A is usually called the "amplitude" (the thing cycles between x = -A and x = +A, so it covers a total distance of 2A in its oscillation) and φ is usually called the "phase" (the thing starts at position A cos(φ)), and ω is called the "angular velocity" (the thing repeats when ω T = 2π, so ω = 2π / T = 2π f, where T is the period and f is the frequency).
The velocity is given by taking one derivative:
v(t) = dx/dt = -A ω sin(ω t + φ)
Its maximums are ± A ω. So the angular frequency ω is given by (A ω)/A = vmax / amplitude.
x(t) = A cos(ω t + φ)
Where A is usually called the "amplitude" (the thing cycles between x = -A and x = +A, so it covers a total distance of 2A in its oscillation) and φ is usually called the "phase" (the thing starts at position A cos(φ)), and ω is called the "angular velocity" (the thing repeats when ω T = 2π, so ω = 2π / T = 2π f, where T is the period and f is the frequency).
The velocity is given by taking one derivative:
v(t) = dx/dt = -A ω sin(ω t + φ)
Its maximums are ± A ω. So the angular frequency ω is given by (A ω)/A = vmax / amplitude.
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An harmonic oscillator describes a position:
x(t) = A cos(ω t + φ)
Where A is usually called the "amplitude" (the thing cycles between x = -A and x = +A, so it covers a total distance of 2A in its oscillation) and φ is usually called the "phase" (the thing starts at position A cos(φ)), and ω is called the "angular velocity" (the thing repeats when ω T = 2π, so ω = 2π / T = 2π f, where T is the period and f is the frequency).
The velocity is given by taking one derivative:
v(t) = dx/dt = -A ω sin(ω t + φ)
Its maximums are ± A ω. So the angular frequency ω is given by (A ω)/A = vmax / amplitude.
x(t) = A cos(ω t + φ)
Where A is usually called the "amplitude" (the thing cycles between x = -A and x = +A, so it covers a total distance of 2A in its oscillation) and φ is usually called the "phase" (the thing starts at position A cos(φ)), and ω is called the "angular velocity" (the thing repeats when ω T = 2π, so ω = 2π / T = 2π f, where T is the period and f is the frequency).
The velocity is given by taking one derivative:
v(t) = dx/dt = -A ω sin(ω t + φ)
Its maximums are ± A ω. So the angular frequency ω is given by (A ω)/A = vmax / amplitude.