A small mass attached to a spring oscillates with simple harmonic motion with amplitude of 70 mm, taking 13 seconds to make 40 complete oscillation. Calculate its angular frequency?
You don't need the amplitude to compute the frequency. The fact that it is a mass and spring is also not needed.
The frequency is 40/13 = 3.08 oscillations per second or "Hz".
Multiply that by 2 pi and you get 19.3 radians/s for the angular frequency.
To calculate the angular frequency of the oscillation, we can use the formula:
Angular frequency (ω) = 2π / Time period (T)
To find the time period, we need to divide the total time taken by the number of complete oscillations:
Time period (T) = Total time / Number of oscillations
In this case, the total time is given as 13 seconds and the number of complete oscillations is given as 40.
So, the time period is:
T = 13 s / 40 = 0.325 seconds
Now, we can substitute this value into the formula to find the angular frequency:
ω = 2π / 0.325 s
Calculating this expression, we find:
ω ≈ 19.25 rad/s
Therefore, the angular frequency of the oscillation is approximately 19.25 rad/s.