Amass of 1000 kg drops from a height of 10 m on a platform of negligible mass. it is desired to design a spring and dashpot on which to mount the platform so that the platform will settle to a new equilibrium position 0.2 m below its original position as quickly as possible after the impact without overshooting. find the spring constant k and the damping constant b of the dashpot. be sure to examine your proposed solution x(f) to make sure that it satisfies the correct initial conditions and docs not overshoot. find, to two significant figures, the time required for the platform to settle within 1 mm of its final position.

k =

b =

t =

Solution:

As per the question:

Mass of the block, m = 1000 kg

Height, h = 10 m

Equilibrium position, x = 0.2 m

Now,

The velocity when the mass falls from a height of 10 m is given by the third eqn of motion:

where

u = initial velocity = 0

g = 10

Thus

Force on the mass is given by:

F = mg =

Also, we know that the spring force is given by:

F = - kx

Thus

Now, to find the damping constant b, we know that:

F = - bv

Now,

Time required for the platform to get settled to 1 mm or 0.001 m is given by:

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.

find the surface area of the sphere to the nearest square unit. use a calculator.

a. 254 in.2

b. 64 in.2

c. 127 in.2

d. 1,018 in.2