A harmonic oscillator has mass 0.530km and an ideal spring with force constant 146N/m .
Find the period, frequency, and angular frequency.
period is 2pisqr(m/k)
frequnecy is 1/t
I assume your mass units are kg, not km. Mikhail's period formula is correct.
The angular frequency (rad/s) is
sqrt(k/m) and the actual frequency is that divided by 2 pi
To find the period, frequency, and angular frequency of a harmonic oscillator, we can use the formula:
Period (T) = 2π√(m/k)
where:
m = mass of the oscillator
k = force constant of the spring
Given:
mass (m) = 0.530 kg
force constant (k) = 146 N/m
Let's calculate the values step by step:
1. Period (T):
Substituting the given values into the formula, we have:
T = 2π√(0.530/146) ≈ 2π√(0.003630) ≈ 2π * 0.06028 ≈ 0.3793 s
2. Frequency (f):
The frequency is defined as the reciprocal of the period, so we can calculate it using the formula:
f = 1/T
Substituting the value of T calculated earlier:
f = 1/0.3793 ≈ 2.636 Hz
3. Angular Frequency (ω):
The angular frequency (ω) is defined as the ratio of 2π multiplied by the frequency, so we can calculate it using the formula:
ω = 2πf
Substituting the value of f calculated earlier:
ω = 2π * 2.636 ≈ 16.556 rad/s
Therefore, for the given harmonic oscillator, the period is approximately 0.3793 seconds, the frequency is approximately 2.636 Hz, and the angular frequency is approximately 16.556 rad/s.