A simple harmonic oscillator executes motion whose amplitude is .20 m and it completes 60 oscillations in 2 minutes Calculate its time period and angular frequency
a. T = 2min/60cycles = 120s/60cycles = 2s/cycles
b. F = 1/T = 1cycle/2s. = 0.50 cycles/s.
= 0.50 Hz.
To calculate the time period and angular frequency of a simple harmonic oscillator, you need to know the number of oscillations completed and the time taken for these oscillations.
Given:
Amplitude (A) = 0.20 m
Number of oscillations (n) = 60 oscillations
Time taken (T) = 2 minutes = 120 seconds
Time Period:
The time period (T) is the time taken for one complete oscillation. It can be calculated by dividing the total time taken by the number of oscillations:
Time Period (T) = Time taken (t) / Number of oscillations (n)
T = T / n
T = 120 seconds / 60 oscillations
T = 2 seconds
Therefore, the time period of the simple harmonic oscillator is 2 seconds.
Angular Frequency:
The angular frequency (ω) is the rate at which the oscillator completes one full oscillation in radians per unit time. It can be calculated by dividing the angular displacement (θ) by the time taken for one complete oscillation (T).
Angular Frequency (ω) = 2π / Time Period (T)
ω = 2π / T
ω = 2π / 2 seconds
ω = π radians per second
Therefore, the angular frequency of the simple harmonic oscillator is π radians per second.