Properties of Oscillation in a Mass-Spring System

What are the key properties of oscillation in a mass-spring system?

1. What is the oscillation amplitude of the system?

2. How do you calculate the phase angle in radians?

3. What is the formula to determine the spring constant in this system?

Answers:

a. The oscillation amplitude is 10 cm, the phase angle is 1.23 radians, and the spring constant is 15.777 N/m.

In a lab experiment involving a 0.4 kg block attached to a massless spring on a frictionless surface, key properties of oscillation were observed. The amplitude of oscillation, measured at 10 cm from the equilibrium position, signifies the maximum displacement of the block during oscillation. The phase angle, calculated based on the initial velocity of 200 cm/s moving to the right, determines the angular position of the block within the oscillation cycle. The spring constant, crucial in defining the system's stiffness, was computed as 15.777 N/m to characterize the spring's behavior.

The equations for position and velocity as functions of time, derived from these properties, allow for the representation of the block's motion. The position equation x(t) = 10cos(2πt + 1.23) and the velocity equation v(t) = -10ωsin(2πt + 1.23) provide insights into the dynamic nature of the mass-spring system. Understanding these oscillation properties enhances our comprehension of the system's behavior and enables precise analysis and prediction of its motion.