Final answer:
The velocity of the body performing simple harmonic motion can be found using the equation v = ω√(A² - x²), where v is the velocity, ω is the angular frequency, A is the amplitude, and x is the displacement from the mean position. Substituting the given values, the velocity is approximately 62.83 m/s.
Step-by-step explanation:
The velocity of a body in simple harmonic motion can be calculated using the equation:
v = ω√(A² - x²)
Where v is the velocity, ω is the angular frequency (equal to 2π times the frequency), A is the amplitude of the motion, and x is the displacement from the mean position. In this case, the mass of the body is given as 20g, the frequency is 10Hz, and the amplitude is 10cm. Converting the mass to kilograms (20g = 0.02kg) and the amplitude to meters (10cm = 0.1m), we can use the equation to find the velocity:
v = (2π * 10Hz)√((0.1m)² - (0.1m)²) = (20π)m/s ≈ 62.83 m/s.