Y Figure 1. Schematic of an elastic pendulum. The grey curve represents the trajectory of the...

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Y Figure 1. Schematic of an elastic pendulum. The grey curve represents the trajectory of the mass. In this assignment, the following is assumed/given: Table 1. Physical quantities in the system. Property Symbol Quantity Unit Item Total mass m 0.2 kg Initial angle 00 0.05 rad Initial angular 0.02 rad/s velocity Initial radius 0.1 m/s velocity Spring Free length 25 B Initial elongation dro 1 m Elastic coefficient k 20 N/m The elastic pendulum swings in one plane, so two dimensional coordinate system is adequate to describe the system. The equation of motion for a harmonic oscillator (elastic pendulum) is in the form of: (t) + a. ((t) C) = 0 (a > 0) a and C are constants, which can vary depending on the characteristics of the system (spring, dimensions, mass, etc), and need to be determined based on the problem at hands. This equation of motion has the following linearised analytical solution when applying the small angle theorem (0 < 5, sin 0, cose 1): 8(t) = A cos(wn t p) + C - Where Angular frequency Amplitude wn = a A = (00-C) + Wn Phase = atan `(00-C) * Wn' Y Figure 1. Schematic of an elastic pendulum. The grey curve represents the trajectory of the mass. In this assignment, the following is assumed/given: Table 1. Physical quantities in the system. Property Symbol Quantity Unit Item Total mass m 0.2 kg Initial angle 00 0.05 rad Initial angular 0.02 rad/s velocity Initial radius 0.1 m/s velocity Spring Free length 25 B Initial elongation dro 1 m Elastic coefficient k 20 N/m The elastic pendulum swings in one plane, so two dimensional coordinate system is adequate to describe the system. The equation of motion for a harmonic oscillator (elastic pendulum) is in the form of: (t) + a. ((t) C) = 0 (a > 0) a and C are constants, which can vary depending on the characteristics of the system (spring, dimensions, mass, etc), and need to be determined based on the problem at hands. This equation of motion has the following linearised analytical solution when applying the small angle theorem (0 < 5, sin 0, cose 1): 8(t) = A cos(wn t p) + C - Where Angular frequency Amplitude wn = a A = (00-C) + Wn Phase = atan `(00-C) * Wn'