Ejercicio Exercise 1 - Simple harmonic motion · Física II URV 2024

Exercise 1 (10 points). Mass-spring system and damped oscillations

A mass of $200\text{ g}$ is suspended from a system of two parallel springs as illustrated below. The elastic constants of the two springs are $k_1 = 0.9\text{ N/m}$ and $k_2 = 1.1\text{ N/m}$, respectively.

At time $t = 0$, the mass is released from rest at a position $-2\text{ cm}$ away from equilibrium. Assuming negligible air resistance:

a.

Determine the equivalent elastic constant of the assembly, as well as the pulsation (angular frequency) and the oscillation period. [2 points]

b.

Write the equation of motion $x(t)$ in SI units (express $x$ in meters). [2 points]

c.

Compute the total mechanical energy of the system at any given moment. How is this energy divided between kinetic and potential forms when the mass reaches $+1\text{ cm}$ from the equilibrium position? [2 points]