Question

A spring with a spring constant k of 100 pounds per foot is loaded with 1-pound weight and brought to equilibrium. It is then stretched an additional 1 inch and released. Find the equation of motion, the amplitude, and the period. Neglect friction.y(t)=equation editorEquation Editorwhere t is time in (seconds) and y(t) is displacement (in feet).Amplitude:equation editorEquation Editorinch(es)

Answer 1

y = 1 cos 10t inch

Step-by-step explanation:

This exercise creates a simple harmonic motion, which is described by the equation.

y = A cos (wt + φ)

The initial load of 1 lb creates a new equilibrium point (y₀), but does not intervene in the movement because it is in equilibrium, the unbalanced force is created by the movement.

The system lengthens 1 inch. Additional this is the breadth

A = 1 in

The angular velocity is given by

w = √ (k / m)

w = √ (100/1)

w = 10 rad / s

The angle φ is determined by the initial conditions

In this case for maximum elongation is released, the speed is zero at this point

v =dy/dt = - A w sin (wt + φ)

0 = A w sin(w 0 + φ)

0 = sin fi

fi = 0

With these results we can write the equation

y = 1 cos (10 t +0)

y = 1 cos 10t inch