Question

1. Derive the vector and scalar equations of motion of the following spring-\damper-mass system with $k$, $c$ and $m$. The incline is frictionless \theta $c$ $m$ $k$ Horizon For the system, determine the circular natural frequency, the critical damping\coefficient, the circular damped natural frequency, period of the damped\vibration with no external driving forces. Show that the mass converges exponentially to the equilibrium position when it is\displaced from the equilibrium position and that $c = 2\sqrt{mk}$.

          1. Derive the vector and scalar equations of motion of the following spring-\damper-mass system with $k$, $c$ and $m$.
The incline is frictionless
\theta
$c$
$m$
$k$
Horizon
For the system, determine the circular natural frequency, the critical damping\coefficient, the circular damped natural frequency, period of the damped\vibration with no external driving forces.
Show that the mass converges exponentially to the equilibrium position when it is\displaced from the equilibrium position and that $c = 2\sqrt{mk}$.

1. Derive the vector and scalar equations of motion of the following spring--mass system with k, c and m.
The incline is frictionless
θc
m
k
Horizon
For the system, determine the circular natural frequency, the critical damping, the circular damped natural frequency, period of the dampedwith no external driving forces.
Show that the mass converges exponentially to the equilibrium position when it isfrom the equilibrium position and that c = 2√(mk).

Added by Christopher S.

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