(1 point) A brick of mass 6 kg hangs from the end of a spring. When the brick is

Question

(1 point) A brick of mass 6 kg hangs from the end of a spring. When the brick is at rest, the spring is stretched by 7 cm. The spring is then stretched an additional 3 cm and released. Assume there is no air resistance. Note that the acceleration due to gravity, g, is g = 980 cm/s2 Set up a differential equation with initial conditions describing the motion and solve it for the displacement s(t) of the mass from its equilibrium postion (with the spring stretched 7 cm) s(t)- (Note that your answer should measure t in seconds and s in centimeters) cm

Explanation / Answer

we know that for a vertical spring

kx = mg => k = mg/x

if s(t) be the downward dosplacement then

ms''(t) = -k s(t)

s(0) = 3 cm ; s'(0) = 0 cm/s

We know that the general eqn is:

s(t) - A cos(wt) + B sinwt

A = 3 cm ; w = sqrt (k/m)t

k = 6 kg x 9.81 / 0.03 = 1960 N/m

w = sqrt (980/7) = 11.83

s(t) = 3 cos(11.83 t)

Related Questions

Navigate

• Browse (All)
• Browse #
• Subjects

---

---

Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.