A particle with a mass of 3.00 10-20 kg is oscillating with simple harmonic motion with a period of 7.00 10-5 s and a maximum speed of 4.50 103 m/s.
(a) Calculate the angular frequency of the particle.
rad/s
(b) Calculate the maximum displacement of the particle.
m
ω=2π/T=2•3.14/7•10⁻⁵=…
x(max) =A.
v(max)=Aω =>
A= v(max)/ω=…
To find the angular frequency of the particle, we can use the formula:
angular frequency (ω) = 2π / period (T)
(a) angular frequency (ω) = 2π / 7.00 * 10^(-5) s
To calculate the maximum displacement of the particle, we can use the formula:
maximum displacement (A) = maximum velocity (v) / angular frequency (ω)
(b) maximum displacement (A) = 4.50 * 10^3 m/s / angular frequency (ω)
Let's calculate each step separately:
(a) Calculation for angular frequency:
ω = 2π / 7.00 * 10^(-5) s = (2π) / (7.00 * 10^(-5)) s ≈ 901,814.18 rad/s
(b) Calculation for maximum displacement:
A = 4.50 * 10^3 m/s / ω = (4.50 * 10^3) m/s / 901,814.18 rad/s ≈ 0.00499 m
Therefore:
(a) The angular frequency of the particle is approximately 901,814.18 rad/s.
(b) The maximum displacement of the particle is approximately 0.00499 m.