A swing is drawn to the side 3m from its equilibrium position and released. The swing is 2m on the other side of the equilibrium position 1.64s later. Find the angular frequency of the SHM.
To find the angular frequency of the Simple Harmonic Motion (SHM), we can use the formula:
ω = 2π/T
where ω is the angular frequency and T is the time period.
In this case, the swing starts from a position 3m from its equilibrium position and swings to a position 2m on the other side in 1.64s.
To find the time period T, we need to consider the time it takes for the swing to swing back and forth. Since the swing started from 3m to the side and swings to a position 2m on the other side, we need to consider the total distance traveled, which is twice the amplitude of the swing.
So, the total distance traveled is 2*3m = 6m.
Now, let's think about the time it takes for the swing to travel this distance. From the information given, we know that it takes 1.64s for the swing to travel from one extreme to the other. This means the swing takes half of this time, or 1.64s/2 = 0.82s to travel from the equilibrium position to one extreme and back to the equilibrium position.
So, the time period T is 0.82s.
Now, we can substitute this value of T into the formula for angular frequency ω:
ω = 2π/0.82s
Calculating this, we find:
ω ≈ 7.64 rad/s
Therefore, the angular frequency of the SHM for the swing is approximately 7.64 rad/s.