Final answer:
To calculate the maximum speed of an oscillating mass, apply the formula v_max = A∙ω, where A is the amplitude and ω is the angular frequency. The % error can be calculated by comparing theoretical and experimental values. To minimize error, improve measurement techniques and equipment precision.
Step-by-step explanation:
To calculate the maximum speed of an oscillating mass, you need to consider the conditions of simple harmonic motion. The maximum speed (v_max) occurs when the mass passes through the equilibrium point, and it can be found using the formula:
v_max = A∙ω
Where A is the amplitude of the oscillation and ω (omega) is the angular frequency. Angular frequency can be calculated using the spring constant k and the mass m with the formula ω = √(k/m).
For example, in the case of a car with mass 900 kg and a spring constant of 6.53×104 N/m that hits a bump and bounces with an amplitude of 0.100 m, the steps to find the maximum velocity are as follows:
To calculate the % error between the calculated value and an experimental value, use the formula:
% Error = ((Experimental Value - Theoretical Value) / Theoretical Value) × 100%
Errors could be due to factors such as air resistance, inaccurate measurements, or friction that were not accounted for in the theoretical model. To improve accuracy, one could refine measurement techniques, reduce friction, or use more precise equipment.