A mass of 16 kg stretches a spring 4.9 cm. The mass moves in a medium that imparts a viscous force of 4 N when the speed of the mass is 1 cm/s. The mass is set in motion from its equilibrium position with an initial upward velocity of 5 cm/s. No external force is applied. Write the IVP so that u would be in meters if solved.

The initial value problem is given by

16 u'' + 400 u' + 3203 u = 0 , u (o) = 0 & u' (0) = 0.05

Explanation:

Given data

m = 16 kg

L = 4.9 cm = 0.049 m

Viscous force F = 4 N

Sped of the mass u' (t) = 1 = 0.01

u (o) = 0

u' (0) = 0.05

We know that

K =

k = 3203

This is the stiffness of the spring.

We know that viscous force F = c u' (t)

Where c = damping constant

C = 400 N

Therefore the initial value problem is given by

m u'' + c u' + k u = 0

16 u'' + 400 u' + 3203 u = 0 , u (o) = 0 & u' (0) = 0.05

the five characteristics of adolescence are biological growth and development, and undefined status, increased decision making, increased pressure and the search of self.

answer: the metamorphic rocks are formed when they are exposed to high pressure and high temperatures. this happens when one of the earth's plates comes in contact with the other plate by traveling in opposite directions, straight into each other or slipping under one another. the friction that is caused by this activity results in   melting of rocks and when it cools they are known as metamorphic rocks. this process needs a controlled amount of pressure and temperature otherwise it may turn into magma.