Damped Oscillations

Purpose:

To explore the dynamics of damped harmonic motion using a mass-spring oscillator.

Description:

This lab consists of 2 parts. In the first part we derive the second order equation,

x'' + 2 x' + 02 x = 0,

(1)

governing the displacement x from equilibrium of a massless spring undergoing damping. Students verify that a solution of (1) is x(t) = A e^-t cos (t - ), where ² = ₀² - ² and A and are arbitrary constants.

In the second part of the lab students set up 2 spring experiments. In the first experiment they collect data to find the spring constant k. In the second experiment they use MBL equipment to record the motion of the oscillator. Using their data they find the frequency of oscillation as well as the 'amplitude' (exponential decay) of the oscillation. The 'amplitude' can then be used to determine the damping parameter . Finally they graph both velocity vs. time and position vs. time on the same plot and comment on the relationship between the graphs.

Materials Needed:

• MBL equipment with distance probe.
• 1 meter rod with clamp.
• 1 metal bar clamp
• 1 set of metric masses
• 1 50g mass holder

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