2. A kilogram maer is attached to the end of the spring with spring constant 2 N/m. Find the equation of motion if the mass is initially released (set in motion) from rest from a point 1 meter above equilibrium position. (Use the convention that displacements measured below the equilibrium position are positive.) (a) Write the initial-value problem which describes the position of the mass. YO:- (b) Find the solution to your initial-value problem from part (a). y:-(0s(2x)
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A 1/2 kilogram mass is attached to the end of the spring with spring constant 2 N/m. Find the equation of motion if
the mass is initially released (set in motion) from rest from a point 1 meter above equilibrium position. (Use the
convention that displacements measured below the equilibrium position are positive.)
(a) Write the initial-value problem which describes the position of the mass.
1/2y"+2y=0 y(0)=-1 y'(0)=0
(b) Find the solution to your initial-value problem from part (a).
y=-cos(2x)
(c) Graph the solution found in (b) on 0 ≤t ≤2π indicating the extreme displacement from equilibrium position on
the y−axis . (Use the convention that displacements measured below the equilibrium position are positive.)
check the image
(d) What type of motion does the solution of the initial value problem describe? (free undamped (simple harmonic)
motion, free overdamped motion, free critically damped motion, or free underdamped (oscillatory) motion)
free undamped
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