Simple Harmonic Motion Problem Amplitude=10cm=0.1m , period=1s, angular frequency= 6.28 rad
What is the maximum speed of the mass during this motion?
To find the maximum speed of the mass in simple harmonic motion, we first need to know the formula for velocity in simple harmonic motion. The formula is:
v = ω * A * cos(ω * t)
Where:
v = velocity
ω = angular frequency
A = amplitude
t = time
In this case, we are given:
Amplitude (A) = 0.1 m
Angular frequency (ω) = 6.28 rad
Time period (T) = 1 s
To find the maximum speed, we need to find the maximum value of velocity (v). The maximum value of cosine function is 1, so the maximum velocity occurs when cos(ω * t) = 1.
To find this value of time (t), we can divide the time period (T) by 4, since the maximum velocity occurs at t = T/4.
t = T/4 = 1/4 = 0.25 s
Now we can substitute the values into the formula to find the maximum velocity:
v_max = ω * A * cos(ω * t)
v_max = 6.28 rad * 0.1 m * cos(6.28 rad * 0.25 s)
v_max ≈ 1.57 m/s
Therefore, the maximum speed of the mass during this motion is approximately 1.57 m/s.