To find the maximum velocity of the mass in simple harmonic motion, we can use the relationship between velocity and amplitude in harmonic oscillators.
The maximum velocity (v_max) occurs when the displacement is at its maximum, which is equal to the amplitude (A) of the motion.
In simple harmonic motion, the relationship between velocity (v) and displacement (x) is given by the equation:
v = ω√(A^2 - x^2)
Where:
- ω is the angular frequency of the oscillation, which is equal to 2π divided by the period (T).
- A is the amplitude of the motion.
- x is the displacement from the equilibrium position.
We are given:
- Period (T) = 0.33 s
- Amplitude (A) = 0.15 m
To find the angular frequency (ω), we can use the relationship ω = 2π/T:
ω = 2π / T = 2π / 0.33 s
Now, substituting the values of ω and A into the equation for velocity (v), when x = A:
v_max = ω√(A^2 - x^2) = ω√(A^2 - A^2) = ω√0 = 0
Therefore, the maximum velocity of the mass is 0 m/s.