For this Exercise we are not on EARTH. Suppose we are on a planet in some solar

Question

For this Exercise we are not on EARTH. Suppose we are on a planet in some solar system in which the acceleration due to gravity is not constant, but can change depending upon what "zone" you are in on the planet. Consider the following situation. A mass of 50 gm stretches a spring 5 cm. If the mass is displaced from equilibrium by moving it downward 20 cm, and if there is no damping, determine the position u(t) of the mass at any time t. (Use g = 5 m/s^2 for the acceleration due to gravity. Let u(t), measured positive downward, denote the displacement in meters of the mass from its equilibrium position at time t seconds.) u(t) = t = pi/14 sec.

Explanation / Answer

Fnet = kx - m g = 0

k(0.05) = (50 x 10^-3) (5)

k = 5 N / m

m w^2 = k

w = sqrt(5 / 0.050) = 10 rad/s

A = 20 cm

u(t) = - A cos(wt)

u(t) = -20 cm cos(10t) ...Ans

u(t) = 0

0 = - 20 cos(10t)

10t = pi / 2

t = pi / 20 sec ......Ans

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